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:

                                    Product A       Product B       Product C
demand for next year .............  24,000 units   25,000 units   12,000 units
selling price per unit ...........    $80             $120            $160
direct material cost per unit ....    $24             $ 21            $ 38
direct labor cost per unit .......    $18             $ 50            $ 38
variable overhead cost per unit ..    $22             $ 25            $ 54 

It takes 0.80 machine hours to produce one unit of Product A; 1.25 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.

Answer 1

	A	B	C
Selling price	80	120	160
less:variable cost
Direct material	24	21	38
Direct labor	18	50	38
variable overhead	22	25	54
Total variable overhead	(64)	(96)	(130)
contribution per unit	16	24	30
Hours required per unit	.80	1.25	1.60
contribution per hour	16/.80=$20	24/1.25=$19.2	30/1.6=18.75
Ranking	1	2	3

Availability and use of hours

Product	Hours used	Hours left for use	Units produced
A	24000*.80= 19200	48000-19200=28800	24000
B	25000*1.25=31250	since available for use is only 28800 ,production of B will be restricted to 28800/1.25 = 23040 units	23040

If Additional overtime is done to manufacture the remaining units of B and c,contribution will be"

	B	C
Selling price	120	160
variable cost	(96)	(130)
Overtime premium	(25)   [50*50%]	(19)    [38*50%]
contribution per unit	(1)	11

since if overtime is done contribution of B will be negative so all of the overtime hours should be used for manufacturing C

Number of units of C that can be manufactured :8000 /1.60 = 5000 units

total number of units of Product C that XYZ Company should
produce in order to maximize its net income : 5000 units