A retail store sells two types of shoes, sneakers, and sandals. The store owner pays $8 for the sneakers and $14 for the sandals. The sneakers can be sold for $10 and the sandals can be sold for $17. The owner of the store estimates that she won't sell more than 200 shoes each month, and doesn't plan to invest more than $2,000 on inventory of the shoes. How many of each type of shoe should be stocked in order to maximize her total monthly profit?

Question

Mathematics

Milagros Rowland

1 October, 08:55

A retail store sells two types of shoes, sneakers, and sandals. The store owner pays $8 for the sneakers and $14 for the sandals. The sneakers can be sold for $10 and the sandals can be sold for $17. The owner of the store estimates that she won't sell more than 200 shoes each month, and doesn't plan to invest more than $2,000 on inventory of the shoes. How many of each type of shoe should be stocked in order to maximize her total monthly profit?

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Jerimiah Pena · Answer 1

The number of sneaker is 133 and sandals is 67.

Step-by-step explanation:

Let the total sneaker = x

Let the total sandals = y

Price of sneaker $8 and price of sandals $14.

Maximum amount that can be invested = $2000

Maximum number of pair of shoes can be sold = 200 shoes.

Here we make two equation; x + y ≤ 200

8x + 14y ≤ 2000

Now solve these two equation for the value of x and y.

x + y = 200

x = 200 - y

now put value of x in 8x + 14y = 2000.

8 (200-y) + 14y = 2000

Y = 66.67 or 67 (round off)

Now put value of Y in x + y = 200.

x = 200 - y

x = 200 - 67

x = 133