A rectangular page is to contain 32 square inches of print. The margins at the t

Question

A rectangular page is to contain 32 square inches of print. The margins at the top and bottom of the page are to be 2 inches wide. The margins on each side are to be 1 inch wide. Find the dimensions of the page that will minimize the amount of paper used. (Let x represent the width of the page and let y represent the height.) x = in y = in A commodity has a demand function modeled by p = 115 - 0.5x and a total cost function modeled by C = 40x + 39.75, where x is the number of units. What price yields a maximum profit? $ per unit When the profit is maximized, what is the average cost per unit? (Round your answer to two decimal places.) $ per unit

Explanation / Answer

xy =32

paper used = (x-2)(y-4)

u = (x-2)(32/x-4)

du/dx= (x-2)(-32/x^2)+((32/x)-4) = 0

x=4

xy =32

y =8

2)

a)

p = 115-0.5x

pc = 115x-0.5x^2

c = 40x+39.5

profit = 115x-0.5x^2- 40x-39.5

dp/dx = 115-x-40

x = 75

p = 115-0.5x = 77.5

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