The above table shows the probability distribution of cake sales at Busy Betty's Bakery.
-Refer to the table above. Busy Betty sells her cakes for $20 each and her constant marginal cost to produce each cake is $12, which is equal to her (constant)average total cost. If she does not sell a cake the day she makes it, she sells it as day- old cake for $10. What is her expected marginal cost of holding the 22nd cake in inventory?

Question

Quizplus · Accepted Answer

Based on the distribution, the probability that Betty will sell all 21 cakes she produces is 0.15. If this happens, then she will not have any more cakes to sell and will have to sell the 22nd cake as day-old cake for $10. Thus, the marginal cost of holding the 22nd cake in inventory is $12 - $10 = $2.

On the other hand, if she does not sell all 21 cakes she produces, then she will sell the remaining cakes as day-old cakes for $10 each. In this case, the marginal cost of holding the 22nd cake is equal to the probability of selling 21 cakes multiplied by the marginal cost of producing the 22nd cake, plus the probability of selling 20 or fewer cakes multiplied by the marginal cost of producing and holding the 22nd cake in inventory.

Marginal cost of producing the 22nd cake = $12
Marginal cost of producing and holding the 22nd cake in inventory = $12 - $10 = $2

Probability of selling 21 cakes = 0.15
Probability of selling 20 or fewer cakes = 1 - 0.15 = 0.85

Expected marginal cost of holding the 22nd cake
= 0.15($12) + 0.85($2)
= $1.80 + $1.70
= $3.50

Therefore, the best choice is to produce only 21 cakes, as the expected marginal cost of holding the 22nd cake is higher than the marginal cost of producing it.

The Above Table Shows the Probability Distribution of Cake Sales