Question

Carmen's Pool Cues has a variable cost of $7.00, a fixed cost of $1,200, and a selling price of $9.00 each.

a. How many units must be sold to make a profit of $300.00? Go to at least three decimals for the intermediate steps, and round your final answer up or down to the nearest whole number (so 18.2 would be rounded as 18, 18.5 would be rounded as 19).

b. How many units must be sold to average $.40 profit per unit? Go to at least three decimals for the intermediate steps, and round your final answer up or down to the nearest whole number (so 18.2 would be rounded as 18, 18.5 would be rounded as 19).

Answer 1

Variable cost = $7.00 per unit

Fixed cost = $1200

Selling price = $9.00

Profit = total revenue – total cost

Total revenue = Selling price * number of units

Total Cost = fixed cost + variable cost = fixed cost + variable cost per unit * number of units

a. Expected profit = $300

Let the number of units = x

Total Revenue = 9*x

Total Cost = 1200 + 7*x

Profit = 9*x – (1200 + 7*x)

= 9*x – 1200 – 7*x

= 2*x – 1200

According to the requirements, Profit = $300

=> 2*x – 1200 = 300

=> 2*x = 300+1200 = 1500

=> x = 1500/2 = 750

Hence, 750 units required to make a profit of $300

b. Average profit = $0.40

Let the number of units = x

Expected profit = 0.40*x

Total Revenue = 9*x

Total Cost = 1200 + 7*x

Hence Profit = 9*x – (1200 + 7*x)

= 9*x – 1200 – 7*x

= 2*x – 1200

According to the requirements, Profit = 0.40*x

=> 0.40*x = 2*x – 1200

=> 2*x – 0.4*x = 1200

=> 1.6*x = 1200

=> x = 750

Hence, 750 units required to make profit of $0.4 per unit.

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