7. Given the following function TR(x)--3x2 + 260x TC(x) = 5,500 + 50x a. Find the...

Question

Question

Answer 1

Answer #1

a) Revenue is maximized where d(TR)/dx = 0 and d²(TR)/dx² should be negative (Second order condition)

d(TR)/dx = -6x + 260 = 0

x = 43.33 (output is maximized at this level)

d²(TR)/dx² = -6 (second order condition is satisfied)

b) TR (max) = - 3 x (43.33)² + 260 x 43.33 = 5633.33

c) Profit (P) = TR - TC = -3x² + 210x - 5500

d) Profit is maximized where d(P)/dx = 0 and d²(P)/dx² should be negative (Second order condition)

dP/dx = -6x + 210 = 0

x = 35 (profit is maximized at this level)

d²P/dx² = -6 (second order condition is satisfied)

e) Maximum profit = - 1825

Answer 2

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