A store sells air filters for $42 each, retail price. The wholesale cost to stoc

Question

A store sells air filters for $42 each, retail price. The wholesale cost to stock the filters is $21 each. The fixed cost associated with acquiring the filters, storing them in inventory, using shelf space, and advertising the filters for sale is $2500.

a. Write a function for the total cost of stocking the filters for sale.

b. Write a function for the total revenue received from selling the filters.

c. Write a system of equations and determine the number of filters that must be sold to break even.

Explanation / Answer

Solution a:

Given, the wholesale cost to stock the filters is $21 each.

Therefore, the wholesale cost to stock "x" number of filters is 21x.

Also, given, the fixed cost associated with acquiring the filters, storing them in inventory, using shelf space, and advertising the filters for sale is $2500.

Therefore, the total cost for stocking the filters for sale is sum of 2500 and 21x.

Let "y" represents the total cost.

So, the function for the total cost of stocking the filters for sale is y = 21x + 2500.

Solution b:

Given, the store sells air filters for $42 each.

Now, we need to find the function for total revenue from selling.

Since, "x" represents the number of air filters, the function for total revenue is y = 42x.

Solution c:

System of equations are y = 21x + 2500

y = 42x

Now, we need to find the number of filters to be sold to break even.

Inorder to find the break even, we need to equate the above two equations.

21x + 2500 = 42x

2500 = 42x - 21x

2500 = 21x

x = 119.0476

Therefore, the store needs to sell 120 air filters to break even.

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