week in review for math 142 week 2jwhitfld/142wir/week2_solutions.pdf · week in review for math...
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Week In Review for Math 142 Week 2
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Week In Review for Math 142 Week 2
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Solution:a) Put the values for the ticket price in L1 and the values for the profit in L2. Then run quadratic regression.
The model that gives the profit as a function of the ticket price is y = 0.0001714x^2 + 0.11486x4.17143
b) By graphing the function, we can use the calculator to compute the maximum value.
So, we know when the ticket price is $335, the company will have a maximum profit of 15.067 million dollars = $15,067,000.
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f)f)
Solutions:a) The Revenue function is R(x) = x*p(x) = x(753x) = 75x3x2.b) The Profit function is P(x) = R(x) C(x) = 75x3x2 (125+6x) = 3x2 + 69x 125.c) To find the maximum revenue, we can graph the revenue function in the calculator and then compute the maximum value.
The output that produces maximum revenue is 12.5 million chips and the maximum revenue is 468.75 million dollars.
d) The wholesale price per chip that produces maximum revenue is found by evaluating p(12.5) = 753(12.5)=37.5. Thus, the wholesale price is $37.5.e) The breakeven points are where R(x)=C(x). We can graph both the revenue function and the cost function in the calculator and then find the points of intersection.
The two breakeven points are (1.982, 136.895) and (21.018, 251.105). So when the company sells 1,982,000 chips, the company will breakeven with cost and revenue equal to $136,895,000. Also, when the company sells 21,018,000 chips, the company will breakeven with cost and revenue equal to $251,105,000.
f) When the company produces and sells between 0 and 1,982,000 chips or more than 21,018,000 chips, they will realize a loss. When the company produces between 1,982,000 and 21,018,000 chips, they will realize a profit.
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