Question

Next Friday, you plan to sell cakes at a bake sale to raise money for your school. You plan to charge $30 per cake, and you anticipate that you will sell 10 cakes. You can either purchase cakes to sell or bake them yourself. If you purchase the cakes, they will cost $23 each. If you bake your own cakes, your cost depends upon the number of cakes you bake, as shown in the table below. Number of cakes you bake Total cost of baked cakes ($) 10 12 8 90 112 136 162 190 1 10 a) How many cakes should you bake? How many cakes should you purchase? Bake cake(s) and purchase O cake(s). b) Given your answer to part a, how much in total will the 10 cakes cost you? c) How much would it have cost you to bake all 10 cakes? d) How much would it have cost you to purchase all 10 cakes?

Answer 1

a)

Number of cakes you bake, Q	Total Cost of baked cake ($), TC	Marginal Cost of cake, MC= Change in TC/Change in Q
0	0
1	10	10
2	22	12
3	36	14
4	52	16
5	70	18
6	90	20
7	112	22
8	136	24
9	162	26
10	190	28

Baking the cake is beneficial as long as marginal cost of baking a cake is lower than cost of purchase i.e. $23. We can see that Marginal cost of baking a cake is lower than cost of purchasing at Q=7 and Marginal Cost of baking a cake is higher than cost of purchasing the cake at Q=8.

So, optimal number of cakes to be baked=7

Number of cakes to be purchased=10-7=3

b)

Cost of baking 7 cakes=$112 (Refer above table)

Cost of purchasing 3 cakes=3*23=$69

Total Cost=112+69=$181

c)

Cost of baking all the 10 cakes=$190 (Refer above table)

d)

Cost of purchasing all the 10 cakes=10*23=$230