Suppose that in addition to repairing your car, you can also spend money adverti

Question

Suppose that in addition to repairing your car, you can also spend money advertising. If you repair your car for Hours and spend A dollars advertising, your benefit(the amount you receive when you sell your car) is B(H,A)=220H-H^2+2A. Both H and A are finely divisible. What is your marginal benefit of repair hours when H=4 and A=100?

Suppose that in Problem above, repair work costs $100 per hour and you have $1500 to allocate between repair work and advertising. Write down the Conostrained optimization Problem you face. What is your best choice of repair hourtising? Interpret the condition that characterizes your best choice in terms of marginal benefits and marginal(opportunity) costs of repair work.

Explanation / Answer

Differentiating B(H,A) with respect to H, we get 220 - 2H.

Marginal benefit at H=4 and A=100 is 212

Second part of problem:

R = 100H Where R= Repair cost

1500 = A+100H

A = 1500 - 100H

Putting this value of A IN B

B(H) = 220H - H2 + 3000 -200H

Differentiating B w.r.t H = 20 - 2H

To maximise the benefit: 20 - 2H = 0

H=10

R=100 * 10 = 1000

A =500

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