11) A mobile company manager wants to maximize the profit for two products. The first mobile yields 800$ per unit and the second one yields 650$.

Assignment submitted by: Nada Zain Assignment submitted by: Nada Zain (Roll# 36) 1(Roll# 36) 1stst Semester Semester Submitted to : Sir Imran Sarwar Submitted to : Sir Imran Sarwar Subject : MathematicsSubject : Mathematics Date : 30Date : 30thth November 2007, Friday November 2007, Friday

Assignment No 2

The combined production level should not exceed 1200 units per month. The demand for product two is at least double the demand of product one. The production level of first product is not more than 150 plus half of the product two.Keeping in mind the above points find the production level for optimum profit. x + y = 1200y ≥ 2xx ≤ 150 + ½y

22) The collective demand of product A and product B should be at least 12000. The demand of B should be at least 5000.A manufacturer wants to maximize the profit of two products. The first product yields a profit of 30$ per unit & the second yields a profit of 40$. Find economically most advantageous production level.A + B = 12000B ≥ 5000

33) The combined production of X & Y should not be less than 200 units. The demand of Y should be at least 100 units. Find the production level for maximum profit.x + y ≥ 200y ≥ 100

44) The total number of students in a class shouldn’t be less than 70.The number of girls should be at least 35. The total number of boys cannot be less than 30. Find the optimum number of students to maximize the profit. If profit from boys is 100$ and from girls is 80$. B + G ≥ 70G ≥ 35B ≥ 30

55) A balanced diet is to provide at least 1500 calories, 30 units of vitamin A, 65 units of vitamin B-12 and 95 units of iron.

An energy bar A provides 600 calories, 45 units of vitamin B-12 and 80 units of iron & energy bar B provides 650 calories, 25 units of vitamin A, 50 units of vitamin B-12 and 60 units of iron.Set a system of linear inequalities that describe minimum daily requirements for calories & vitamins.

66) The profit of 3 factories of a MNC should be at least 5 million$, 6 million$ and 8 million$ respectively.The product S yields a profit of 1000, 4000 and 2000 in factory 1, 2 and 3 respectively.The product T yields a profit of 7000 and 3000 in factories 1 & 3 respectively.Find the most favorable number of production to maximize the profit.

77) The joint production of product E & product F should not be less than 1850 units. The demand of F should be at least 1600 units. Find the production level for highest profit.E + F ≥ 1850F ≥ 1600

88) The total production of three products of a factory shouldn’t be more than 7000 units. The number of product A should be at least 2800 units. The total production of B cannot be less than 2500 units. The total production of C cannot be less than 1500units. Find the optimum production to maximize the profit. If profit from product A is 420$, from B 110 and from product C is 85$. A + B + C ≤ 7000B ≥ 2500C ≥ 1500

99) Collective demand of product X and product Y should be at least 2000. The demand of Y should be at least 900.The production of X cannot be greater than1220 units.A manufacturer wants to maximize the profit of these two products. The first product yields a profit of 75$ per unit & the second yields a profit of 90$. Find economically most cost-effective production level.x + y ≥ 2000y ≥ 900x ≤ 1220

1010) Sony decides to increase the production of two products. The first product yields 880$ per unit and the second one yields 920$.The joint production level should not exceed 10,000 units per month. The demand for product two is at least half the demand of product one. The production level of first product is not more than 100 plus 2 times of the product two. Find the production level for best possible profit.A + B ≤ 10000B ≥ ½ AA ≤ 2B + 100

1111) The collective production of M & N should not be more than 8500 units. The demand of M is 4100 units. The demand of M is not more than 100 plus two-thirds of product N. The production of N cannot go beyond 3800 units. Find the production level for most profit.M + N ≤ 8500M = 4100M ≤ 100 + 2/3 NN ≤ 3800

1212) The combined production of A & B should not be less than 3200 units. The demand of A should be at least 1000 units. The production of A can’t exceed 2000 units. Find the most profitable production level.A + B ≥ 3200

A ≥ 1000A ≤ 2000

1313) The profit of 3 factories should be at least 56000$, 921000$ and 420000$ respectively.The product Q yields a profit of 9000 and 6200 in factories 1 & 3 respectively.The product R yields a profit of 2200, 6500 and 1500 in factory 1, 2 and 3 correspondingly.Find the most favorable number of production to get the most profit.

1414) The mutual making of product 1 & product 2 should not be under 1850 units. The making of 1 can’t exceed 880 units. The demand of 2 is no less than 20 plus production of 2. Find the production level for highest profit.A + B ≥ 1850A ≤ 880B ≥ 20 + A

1515) The entire production of three products of a factory shouldn’t be above 1400 units. The number of product X should be at least 550 units. The total production of Y cannot be more than 690 units. The total production of Z cannot be less than 400units. Find the best possible production to maximize the profit. If profit from product X is 40$, from Y 25$ and from product Z is 38$.X + Y + Z ≥1400X ≥ 550Y ≤ 690Z ≥ 400

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16) The collective demand of product L and product M should be at least 4200. The demand of M should be at least 2100.The demand of L is 300 plus half the demand of M.A manufacturer wants to maximize the profit of two products. The first product yields a profit of 50$ per unit & the second yields a profit of 65$. Find most profitable production level.

L + M ≥ 4200M ≥ 2100L = 300 + ½ M

1717) The liquid portion of a diet should provide at least 300 calories, 36 units of vitamin A, 90 units of vitamin B-12 and 90 units of Vitamin C.A cup of dietary drink A provides 120 calories, 65 units of vitamin B-12 and 72 units of vitamin C & dietary drink B provides 150 calories, 25 units of vitamin A, 50 units of vitamin B-12 and 65 units of vitamin C.Set a system of linear inequalities that describe minimum daily requirements for calories & vitamins.

1818) The combined production of product D and product E cannot be more than 8600. The demand of E should be no less than 4100.A firm wants to maximize the profit of two products. The first product yields a profit of 400$ per item & the second yields a profit of 605$. Find most profitable production level.

1919) A company decides to increase the profit of two products. The first product yields 50$ per unit and the second one yields 20$.The joint production level should not exceed 2000 units per month. The demand for product two is not more than 4 times the demand of product one. The production level of first product is not more than 15 plus 3 times of the product two. Find the production level for best achievable profit.

2020) The communal demand of product A and product B should be at least 6000. The demand of B should be at least 2500.A manufacturer wants to maximize the profit of two products. The first product yields a profit of 20$ per unit & the second yields a profit of 35$. Find most profitable production level.

2121) The mutual making of product 1 & product 2 should not be under 1850 units. The making of 1 can’t exceed 880 units. The demand of 2 is no less than 900 units. The demand of product 2 can’t exceed 30

plus demand of product 1.Find the production level for maximum profit.A + B ≤ 1850A ≤ 880B ≥ 900B ≤ 30 + A

2222) A producer decides to increase the profit of three products. The first product yields 510$ per unit, the second one yields 430$ and the third yields 15$ plus the profit of product 2.The joint production level should not exceed 18000 units per month. The demand for product two is not more than half the demand of product one. The production of product two should be at least 300 units per month. The production level of first product is not more than two times of the product three. Find the production level for best attainable profit.

2323) The combined production of J & I should be more than 5500 units. The demand of J should be at least 2100 units. The production of I can’t exceed 2520 per month. The production of J should be at most 60 units more than production of I. Find the production level for maximum profit. I + J ≥ 5500J ≥ 2100I ≤ 2520J ≤ 60 + I

2424) The profit of 3 factories should be no less than 19000$, 21000$ and 28000$ respectively.The product A yields a profit of 6500 and 4200 in factories 1 & 2 respectively.The product B yields a profit of 2100, 1500 and 2500 in factory 1, 2 and 3 correspondingly.Find the most advantageous number of production to get the most profit.

2525) The joint production of product 1 product 2 and 3 should not be under 10500 units. The making of 3 is 560 units. The demand of 2 is no less than 900 units. Demand of 1 is at least 30 plus demand of 3. Find the production level for highest profit.

A + B + C ≥ 10500C = 560B ≥ 900A ≥ 30 + C

2626) The combined demand of Honda motorcycles and bicycles is not less than 4500 units. The manufacture of motorcycles can’t exceed 2100 units. The demand of cycles is no less than 2600 units. Demand of motorcycles is 500 less than the demand of cycles. Find the optimum manufacture for highest profit.X + y ≥ 4500X ≤ 2100Y ≥ 2600X = 500 - y

2727) Manager of Nestle Pakistan wants to increase the profit of two products. The first mobile yields 80 Rs. per unit and the second yields 65 Rs.The combined production level cannot exceed 12500 units per month. The demand for product two is at least double the demand of product one. The production level of first product is not more than 1200 minus double of the product two.Find the production level for optimum profit. x + y = 1200y ≥ 2xx ≤ 1200 - 2y

2828) The combined production of product 1 & product 2 should not be more than 2000 units. The making of 2 is 1230 units. The demand of 2 is no less than 990 units. Demand of 1 is at most 150 plus demand of 2. Find the production level for highest profit.A + B ≤ 2000B = 1230B ≥ 990A ≤ 150 + B

2929) A machine can produce product A by using 2 units of a chemical and 1 unit of a compound or can produce product B by using 1 unit of chemical and 2 units of a compound. Only 400 units of chemical and 500 units of the compound are available. The profit per unit of A & B are 3$ and 2$ respectively. Maximize the profit function.

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30) A candy factory manager wants to increase the production and profit of two candy bars “Bon Bon” and “Buttercups”. The demand for “Bon Bon” is at least 6150 units. The production of “buttercups” can’t exceed 5800 units. The production of “Bonbons” should be not less than 400 plus the production of “Buttercups”. If the profit from bonbons is 0.5$ per unit and the profit from “buttercups” is 0.75$ per unit. Find the optimum production level to maximize the profit.A ≥ 6150B ≤ 5800 A ≥ 400 + B

3131) “Boeing” decides to design a new airplane “Boeing 714”. According to calculation its seats cannot exceed 385. The demand for first class seats is at least 24 seats. The business class seats can’t be more than 8 plus number of first class seats. The economy seats should be at least 310. If the first class makes the highest profit and economy class the least. What should be number of seat for best possible profit?F ≥ 24B ≤ 8 + FE ≥ 310

3232) The joint production of product 1 & product 2 should be more than 2569 units. The making of 2 is 1547 units. The demand of 2 is no less than 1500 units. Demand of 1 is at most 150 plus demand of 2. Find the production level for highest profit. A + B ≥ 2569B = 1547B ≥ 1500A ≤ 150 = B

3333) The combined demand of “Nadec” chocolate flavor milk and Vanilla flavor milk is not less than 6500 units. The manufacture of choco milk can’t exceed 3150 units. The demand of vanilla milk is no less than 2820 units. Demand of choco milk is 210 more than the demand of vanilla milk. Find the optimum manufacture for maximum profit.C + V ≥ 6500C ≤ 3150V ≥ 2820C = 500 + V

3434) The combined making of big registers & medium size registers of a “Rizvi paper factory” can’t be more than 5500 units per month. The

demand of medium size registers should be at least 2100 units. The production of big registers can’t exceed 2520 per month. The production of medium size registers should be at most 60 units more than production of big registers big registers. Find the manufacture level for greatest profit. B + M ≥ 5500M ≥ 2100B ≤ 2520M ≤ 60 + B

3535) The total number of audience at “Sydney Opera House” shouldn’t be more than 375.The number of VIP guests should be at most 105. The total number of common people is not less than 260. Find the optimum number of students to maximize the profit. If profit from VIP guests is 100$ and from common people is 80$. V + C ≥ 70V ≤ 105C ≥ 260

3636) “Sony” has a capacity of collective production of 6010 of Sony Walkman and Sony mini Hi-fi. The demand Walkman is not more than 2100 units. The demand for hi-fi is at least 60 less than two time of demand of Walkman. The production of hi-fi can’t exceed 4500 units monthly.Find the best profitable production level. W + H ≥ 6010W ≤ 2100H ≥ 60 - 2WH ≤ 4500

3737) A textile machine can make shirt A by using 2 feet of fabricX and 1 foot of a fabric Y or can produce shirt B by using 1 foot of fabricX and 2 feet of a fabric Y. Only 400 feet of fabricX and 500 feet of the fabric Y are available. The profit per unit of A & B are 15$ and 22$ respectively. Maximize the profit function.

3828) The combined production of product 1 & product 2 should not be more than 2000 units. The making of 2 is 1230 units. The demand of 2 is no less than 990 units. Demand of 1 is at most 150 plus demand of 2. Find the production level for highest profit.A + B ≤ 2000B = 1230

B ≥ 990A ≤ 150 + B

3929) A machine can produce product A by using 2 units of a chemical and 1 unit of a compound or can produce product B by using 1 unit of chemical and 2 units of a compound. Only 400 units of chemical and 500 units of the compound are available. The profit per unit of A & B are 3$ and 2$ respectively. Maximize the profit function.

4040) “Victoria tourism ships” decides to make a new Cruise ship “Mary Sail 1”. According to calculation its rooms cannot exceed 175. The demand for luxury rooms is at least 24 . The regular economic rooms can’t be more than 8 minus 6 times the number of luxury rooms. What should be number of seat for best possible profit?L + R = 175L ≥ 24R ≤ 8 - 6L

4141) The combined demand of “Kellogg’s” chocolate flavor corn flakes and regular plain corn flakes is not less than 3210 boxes. The manufacture of choco flakes can’t exceed 1150 boxes. The demand of regular cereal is no less than 1820 boxes. Demand of choco cereal is 210 more than the demand of plain cornflakes. Find the optimum manufacture for maximum profit.

C + R = 3210C ≤ 1150R ≥ 1820C = 210 + R

4242) The joint manufacture in “IKEA” of chairs & computer desk is above 850 units. The making of chairs can’t exceed 410 units. The demand of desks is no less than 395 units. The demand of desks can’t exceed 30 plus demand of product 1.Find the production level for maximum profit.C + D ≤ 850C ≤ 410D ≥ 395D ≤ 30 + C

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43) The combined production of product Q and product R cannot be more than 7100. The demand of Q should be no less than 4250.A firm wants to maximize the profit of two products. The first product yields a profit of 4.0$ per item & the second yields a profit of 6.5$. Find most profitable production level.

4444) A company decides to increase the profit of two products. The first product yields 6.75$ per unit and the second one yields 8.25$.The joint production level should not exceed 12500 units per month. The demand for product two is not more than 4 times the demand of product one. The production level of first product is not more than 15 plus 3 times of the product two. Find the production level for best achievable profit.

4545) The collective demand of product A and product B is at least 6000. The production of B can be at most 2500.A manufacturer wants to maximize the profit of two products. The first product yields a profit of 2.0$ per unit & the second yields a profit of 3.5$. Find most profitable production level.

4646) The mutual making of product 1 & product 2 should not be under 7654 units. The making of 1 can’t exceed 2200 units. The demand of 2 is no less than 2510 units. The demand of product 2 can’t exceed 30 plus demand of product 1.Find the production level for maximum profit.A + B ≤ 7654A ≤ 2200B ≥ 2510B ≤ 30 + A

4747) A producer decides to increase the profit of three products. The first product yields 5.0$ per unit, the second one yields 4.5$ and the third yields 1.75$ plus the profit of product 2.The joint production level should not exceed 18000 units per month. The demand for product two is not more than half the demand of product one. The production of product two should be at least 300 units per month. The production level of first product is not more than two times of the product three. Find the production level for best attainable profit.

4848) The combined production of “Reebok” joggers & sandals should be more than

5500 units. The demand of joggers should be at least 2100 units. The production of sandals can’t exceed 2520 per month. The production of joggers should be at most 60 units more than production of sandals. Find the production level for maximum profit. S + J ≥ 5500J ≥ 2100S ≤ 2520J ≤ 60 + S

4949) McDonalds wants to increase the production and profit of two products “McArabia” and “BigMac”.The demand of “McArabia” is not less than 165 per day. Demand of “BigMac” can’t exceed 20 plus two thirds of “McArabia”. The maximum production of “BigMac” is 72 per day. The profit from “McArabia” and “BigMac” is 0.75$ and 1.0$ respectively. Find the optimum making of both of the above products for best possible profit.

5050) The dual production of footballs & basketballs at “m & m” sport goods factory is more than 3150 units. The manufacture of 2 is 1547 units. The demand of 2 is no less than 1500 units. Demand of 1 is at most 150 plus demand of 2. Find the production level for highest profit. A + B ≥ 3150B = 1547B ≥ 1500A ≤ 150 + B