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

Solution(A)-

As you can see Machine is taking 2 machine hours to produce one unit of Alpha ,while Delta is produced in 2.5 hours per unit. As you can see there is limited machine hours reserved which is 500 hours and the contribution margin of both goods is not having much difference. So Slavin Corporation should produce alpha unit fullest subjected to the market demand which is 160 units and rest machine-hours should be used in producing delta good.

Machine hours for producing 160 units of alpha

= 160 x 2 = 320 hours

Rest machine-hours should be used in producing delta good

= (500-320) hours / 2.5 hours = 72 units

So company should produce 160 units of Alpha and 72 units of Delta to Maximise the profit.

Solution (B)-

Monthly profit in current production stage = $620

Monthly Profit after optimal production quantity has opted =

= $ 59 x 160 units + $ 63 x 72 units - Fixed Cost ( 7900+4900)

= $ 1176

So the monthly profit after opting for optimum production quantity will be $ 1176 monthly.

which will be $ 556 higher than before.

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