Toy Productions makes toy trucks from steel according to Q = 50 + 100S - 0.5S².If steel costs $49 and toy trucks sell for $7,the optimal level of steel usage is:

Question

Quizplus · Accepted Answer

To find the optimal level of steel usage, we need to maximize the profit function:

Profit = (Revenue) - (Cost of Steel)

Revenue = Price of each toy truck x Quantity produced
Revenue = $7Q

Cost of Steel = Price of Steel x Quantity of Steel used
Cost of Steel = $49S

Profit = $7Q - $49S

We can maximize this function by taking the derivative with respect to S and setting it equal to zero:

dProfit/dS = -49 + 100U1P12 - S1P0 = 0
Solving for S, we get:
S = 93

Therefore, the optimal level of steel usage is 93.

Toy Productions Makes Toy Trucks from Steel According to Q