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 elther purchase cakes to sell or bake them yourself. If you purchase the cakes, they will cost $27 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 Total cost of you bake baked cakes (S) 1e 36 52 78 9e 112 136 162 19e 18 a) How many cakes should you bake? How many cakes should you purchase? Bake cakefs) and purchase 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?

Answer 1

(a)

Following table shows the marginal cost schedule -

Number of cakes you bake	Total cost of baked cakes ($)	Marginal Cost
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

If cakes are purchased then they cost $27 per cake.

So, the person should bake that number of cakes up to which marginal cost is less than the purchase price of cake from outside.

The above table shows that up to baking of 9 cakes, marginal cost of baking cake yourself is less than the purchase cost.

So,

We should bake 9 cakes.

We should purchase 1 cake.

(b)

The total cost of baking 9 cakes is $162.

The purchase cost of 1 cake is $27.

So,

The total cost of 10 cakes is $189.

(c)

The total cost of baking all 10 cakes is $190.