Question

TEST TOMORROW 33. Mid Town Sports Apparel has found that it needs to sell golf hats at $2.75 each to be competitive. It costs $2.12 to produce each hat, and weekly overhead is $3,000. a. Let x be the number of hats produced each week. Express the average cost (including overhead) of producing one hat as a function of x. b. Solve algebraically to find the number of golf hats that must be sold each week to make a profit. Support your answer graphically. c. How many golf hats must be sold to make a profit of $1,000 in one week. Explain your answer.

Answer 1

a. The total cost is the sum of variable and fixed cost. So the average cost of each hat is simply total cost divided by x:

ave cost = (2.12 x + 3000) / x

 

b. Total cost should be equal to Income:

2.12 x + 3000 = 2.75 x

Solve for x:

x = 4762 units

 

c. Profit is income minus total cost:

Profit = 2.75 x – (2.12 x + 3000)

1000 = 2.75x – 2.12 x – 3000

Solving for x:

x = 6439 hats