Jane Persico, facility engineer at the El Paso plant of Computer Products Corporation (CPC), is studying a process selection decision at the plant. A new printer is to be manufactured and she must decide whether the printer will be auto assembled or manually assembled. The decision is complicated by the fact that annual production volume is expected to increase by almost 50% over three years. Jane has developed these estimates for two alternatives for the printer assembly process:



Auto-Assembly ProcessManual Assembly Process
Annual fixed cost
$690,000$269,000
Variable cost per product
$29.56$31.69
Estimated annual production


(in number of products):Year 1152,000152,000

Year 2190,000190,000

Year 3225,000225,000

a.Which production process would be the least-cost alternative in Years 1, 2, and 3?
Solution
C(x) = Fixed cost + Variable cost(x)
Year 1
CA = 690,000 + 29.56(152,000) = $5,183,120
CM = 269,000 + 31.69(152,000) = $5,085,880 (least-cost alternative)
Year 2
CA = 690,000 + 29.56(190,000) = $6,306,400
CM = 269,000 + 31.69(190,000) = $6,290,100 (least-cost alternative)
Year 3
CA = 690,000 + 29.56(225,000) = $7,341,000 (least-cost alternative)
CM = 269,000 + 31.69(225,000) = $7,399,250

b.How much would the variable cost per unit have to be in Year 2 for the auto-assembly process to justify the additional annual fixed cost for the auto-assembly process over the manual assembly process?