Always Round Tire's New Division, Start-Up Batteries, Finds They Have

Question

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The Answer is Using a calculus approach, marginal cost is the first derivative of TC: MC = 2 + 4Q. From the demand curve, we know that MR = 130 - 4Q. Setting MR=MC and solving for Q yields the profit maximizing output of Q= 16 batteries per day. To sell this quantity of batteries the price should be $98 per battery. The resulting total cost will be $844 per day and total revenue $1,568, yielding a profit.
If the division operates as a Revenue Center, it will maximize total revenue. Assuming it has pricing authority, the division will choose a price and output accordingly. Maximum total revenue occurs at an output where MR = 0, or 130-4Q = 0, or Q=32.5 batteries. If the division operates as a cost center with a target of Q=20, TC = 300 + 2(20) + 2(20)² = $1,140. The cost per battery is $1,140/20 = $57.

Always Round Tire's New Division, Start-Up Batteries, Finds They Have

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