Question

XYZ Company produces three products, A, B, and C. XYZ's plant capacity is limited to 48,000 machine hours per year. The following information is available for planning purposes: demand for next year ..... selling price per unit ..... direct material cost per unit direct labor cost per unit .. variable overhead cost per unit Product A 21,000 units $80 $24 $18 Product B 28,000 units $120 $ 22 $ 50 $ 25 Product C 35,000 units $160 $ 36 $ 62 $ 33 $22. It takes 0.80 machine hours to produce one unit of Product A; 1.20 machine hours to produce one unit of Product B; and 1.60 machine hours to produce one unit of Product C. Assume that XYZ Company can work its plant overtime for 8,000 additional machine hours. Overtime premiums will add 50% to direct labor costs. Calculate the total number of units of Product C that XYZ Company should produce in order to maximize its net income.

The problem said that it "will add 50% to direct labor cost". However, I got a negative contribution margin of victory product C in my calculation so I was confused.

Answer 1

A) Maximum manufacturing capacity of 'product C'

Without Overtime	with overtime
48000 machine hours ÷ 1.60 machine hrs. p.u. = 30000 units	(48000+8000) m/c hrs ÷ 1.60 m/c hrs p.u. = 35000 units

B) Computation of variable cost per unit

Without overtime	With overtime
Direct material cost p.u 36 direct labour cost p.u. 62 Variable OH p.u. 33 Variable cost p.u 131	Direct material cost per unit 36 Direct labour cost per unit 62 Overtime premium 31 Variable OH p.u. 33 Variable cost per unit 162

C) Computation of profit/ (loss) at different production levels

S.No.	Particulars	30000 units of production	35000 units of production
A	Sales	4800000           ($160 × 30000)	5600000     ($160×35000)
B	Variable cost	3930000           ($131 × 30000)	5670000          ($160 × 35000)
C	Profit/(loss)    A-B	870000	-70000

Since at 35000 units level of production it shows loss of 70000 , hence it is profitable for the company to produce up to 30000 units of production.