Question 3 1 pts A mill producing steel plate has fixed cost

Question 3 1 pts A mill producing steel plate has fixed costs of $100,000 per week and variable costs of $0.15 per pound of steel plate produced. If the steel plate sells for $0.77 per pound, how many pounds must be produced each week for the plant to breakeven? Express your answer in pounds to the nearest 1,000 pounds.

Solution

Question 3

Let amount of steel plates to be produced to breakeven be x pounds

Total fixed cost = $100,000

Variable cost = $0.15 per pound of steel plates

Total variable cost = $0.15 * x = $0.15x

Calculate the total cost at breakeven -

Total cost = TFC + TVC = $100,000 + $0.15x

Price per pound = $0.77

Calculate the total revenue at breakeven -

Total revenue = Price * Breakeven quantity = $0.77 * x = $0.77x

Equating total cost at breakeven and total revenue at breakeven to ascertain breakeven quantity -

TR = TC

0.77x = 100,000 + 0.15x

0.62x = 100,000

x = 161,290.32

Rounding to the nearest 1,000 pounds

x = 161,000 pounds

So,

The plant must produce 161,000 pounds of steel plates each week to break-even.