Suppose a business can sell x gadgets for $p = 250 - 0.01 x$ dollars apiece, and it costs the business $c ( x ) = 1000 + 25 x$ dollars to produce the $x$ gadgets. Determine the production level and cost per gadget required to maximize profit.
A) 11,250 gadgets at $137.50 each
B) 13,750 gadgets at $112.50 each
C) 10,000 gadgets at $150.00 each
D) 111 gadgets at $248.89 each

Question

Quizplus · Accepted Answer

To maximize profit, set marginal revenue equal to marginal cost. The revenue function is $R(x) = x(250 - 0.01x)$ and the cost function is $C(x) = 1000 + 25x$. Solving for $x$ gives 11,250 gadgets, and the price per gadget is $p = 250 - 0.01(11,250) = 137.50$.

Suppose a Business Can Sell X Gadgets For p=250−0.01xp = 250 - 0.01 xp=250−0.01x

Suppose a Business Can Sell X Gadgets For $p = 250 - 0.01 x$