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

Paige Mccoy

Mathematics

25 August, 15:05

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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Answers (1)

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Sammy Murphy · 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