Question

XYZ Company produces two products, A and B. For the coming
period, 140,000 machine hours and 210,000 direct labor hours
are available. Information on the two products appears below:

                                    Product A     Product B
selling price per unit ...........    $9.00         $8.00
variable costs per unit ..........    $2.00         $5.00
machine hours per unit ...........     5.00          2.00
direct labor hours per unit ......     3.00          6.00

Calculate the number of units of Product B that should be
produced in order to maximize net income.

Answer 1

Statement of Contribution per unit:

	A	B
Selling price per unit	9	8
Variable cost per unit	-2	-5
Contribution	$7	$3
Labor hours per unit	3	6
Contribution per labor hour	$2.33	$0.5
Ranking for production (A)	I	II
Machine hours per unit	5	2
Contribution per machine hour	$1.4	$1.5
Ranking for production (B)	II	I

Both the resources have opposite ranking.

Let the no. of units of Product A and B to be produced be X, and Y respectively.

Labor hours   3X + 6Y = 210,000

Machine hours 5X + 2Y = 140,000

Solving the above two equations,

Y = 26,250 units

Hence the no. of units of product B to be produced to maximize net income = 26,250 units.