Question

Slavin Corporation manufactures two products, Alpha and Delta. Each product requires time on a single machine. The machine has a monthly capacity of 500 hours. Total market demand for the two products is limited to 160 units (each) monthly. Slavin is currently producing 110 Alphas and 110 Deltas each month. Cost and machine-usage data for the two products are shown in the following table, which Slavin managers use for planning purposes.

	Alpha			Delta			Total
Price	$	120		$	150
Less variable costs per unit
Material		19.5			34.5
Labor		25.5			37.5
Overhead		16			15
Contribution margin per unit	$	59		$	63
Fixed costs
Manufacturing							$	7,900
Marketing and administrative							$	4,900
							$	12,800
Machine hours per unit		2.0			2.5
Machine hours used								495
Machine hours available								500
Quantity produced		110			110
Maximum demand		160			160
Profit	$	620

Required:

a. What is the optimal production schedule for Slavin? In other words, how many Alphas and Deltas should the company produce each month to maximize monthly profit?

b. If Slavin produces at the level found in requirement (a), how much will monthly profit increase over the current production schedule?

Answer 1

Since machine hours is the constraint, product with maximum contribution margin per machine hour should be produced first and then remaining time should be used to produce the other product.

	Alpha	Delta
Contribution Margin per unit (A)	59	63
Machine hours per unit (B)	2.0	2.5
Contribution Margin per hour (A/B)	29.5	25.2

Hence, 160 units (full demand) of Alpha should be produced first

Remaining machine hours = 500 – 160*2 = 180 hours

Units of Delta = 180/2.5 = 72 units

To maximise profit, 160 Alphas and 72 deltas should be produced

b.Monthly profit = 59*160 + 63*72 – 12,800

= $1,176

Increase in profit = $1,176-620 = $556