Question

The Pampered Pooch sells high-end pet furniture, specializing in small breed dogs. The most popular item is the memory foam dog bed, with the following demand curve: Q = 21,100 – 215(P). While expensive, the bed comes with a washable cover and free shipping. Variable costs run at $42. At what quantity sold will total contribution margin be maximized? Round your answer to the nearest dog bed.

Answer 1

Q = 21100 - 215P

P = (21100 - Q) / 215

TR = P*Q

TR = [(21100 - Q) / 215] * Q

TR = (21100Q - Q2 ) / 215.

Variable cost: VC = 42Q

Contribution margin: C = TR - VC

C = [(21100Q - Q2 ) / 215] - 42Q

C = (21100 Q / 215) - (Q2 / 215) - 42Q

To maximize the contribution margin, put dC /dQ = 0

dC / dQ = (21100/ 215) - (2Q/ 215) - 42 = 0

-----> 2Q / 215 = (21100 / 215) - 42

2Q = 215 * [(21100 /215) - 42]

2Q = 21100 - (215) (42)

2Q = 21100 - 9030

2Q = 12070

Q = (12070 / 2)

Q = 6035

Hence, contribution margin is maximized at 6035 units.