Question

Two currently owned machines are being considered for the production of a part. The capital investment associated with the machines is about the same and can be ignored. The important differences between the machines are their production capacities (production rate × available production hours) and their reject rates (percentage of parts produced that cannot be sold). Consider the following table:

	Machine A	Machine B
Production rate	100 parts/hour	130 parts/hour
Hours available for production	7 hours/day	6 hours/day
Percent parts rejected	3%	10%

The material cost is $6.00 per part, and all defect-free parts produced can be sold for $12 each. (Rejected parts have negligible scrap value.) For either machine, the operator cost is $15.00 per hour and the variable overhead rate for traceable costs is $5.00 per hour.

(a) Assume that the daily demand for this part is large enough that all defect-free parts can be sold. Which machine should be selected? (b) What would the percent of parts rejected have to be for Machine B to be as profitable as Machine A?

Answer 1

a) The machine that will maximize the profit per day should be selected.

Profit per day= revenue per day-cost per day

=(production rate)x(production hours)x($12/part)x[1-(%rejected/100)]-(production rate)(production hours)($6/part)-(production hours)($15/hour+$5/hour)

Machine A-(100 parts/hour)(7hours/day)($12/part)(1-0.03)-(100 parts/hour)(7 hours/day)($6/part)-($7 hours/day)($15/hour+$5/hour) = $3808 per day.

Machine B-(130 parts/hour)(6 hours/day)($12/part)(1-0.10)-(130/part)(6 hours/day)($6/part)-(6 hours/day)($15/hour+$5/hour) = $3624 per day.

Therefore,Machine A should be selected to maximize profit per day.

b) Set the profit per day of Machine A = profit per day of Machine B and solve for X to find the breakeven percent of parts rejected for Machine B.

$3808/day = (130parts/hour)(6 hours/day)($12/part)(1-X) - (130 parts/hour)(6 hours /day)($6/part) - (6 hours/day)($15/hour+$5/hour)

Solving,we get X= 0.08,so the percent of parts rejected for Machine B cannot be higher than 8% for it to be as profitable as Machine A