Question

Consider a mill that took $100,000 to build and produces corn flour from purchased hominy. A stone (14 lbs) of hominy costs $3.50 and yields 13 pounds of corn flour, which sells for $1 per pound. Additionally, a worker can produce 20 pounds per hour at an hourly wage of $10. Using algebra and/or Excel, answer the following questions:

(a) What is the break-even quantity?

(b) What is the maximum wage that can be offered without incurring a loss?

(c) What is the break-even quantity if the price of hominy increases to $4 per stone?

Answer 1

Fixed cost = $100,000

Selling price per pound of corn = $1

Variable costs per pound:

Cost of hominy = 3.5/13 = 0.27

Cost of labour = 10/20 = 0.5

Total variable cost = 0.77

Contribution = Selling price- Variable cost = 1-0.77 = 0.23 per pound

a: Break even quantity = Fixed cost/ Contribution per unit

= 100000/ 0.23

= 434782.61

or 434783 pounds of corn.

b: Maximum wage = current wage + contribution

= 0.5+ 0.23

= 0.73 per pound

Hence hourly wage = $0.73* 20 pounds

= $14.60

c:

Fixed cost = $100,000

Selling price per pound of corn = $1

Variable costs per pound:

Cost of hominy = 4/13 = 0.31

Cost of labour = 10/20 = 0.5

Total variable cost = 0.81

Contribution = Selling price- Variable cost = 1-0.81 = 0.19 per pound

Break even quantity = Fixed cost/ Contribution per unit

= 100000/ 0.19

= 526315.79

or 526316 pounds of corn.