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.

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

example 2 – simplify: step 1: completely factor both the numerators and denominators of all fractions. step 2: change the division sign to a multiplication sign and flip (or reciprocate) the fraction after the division sign; essential you need to multiply by the reciprocal. step 3 : cancel or reduce the fractions.

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step-by-step explanation: