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 115 Alphas and 115 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 $ 125 $ 150 Less variable costs per unit Material 17 34 Labor 24 36 Overhead 16 15 Contribution margin per unit $ 68 $ 65 Fixed costs Manufacturing $ 7,300 Marketing and administrative $ 4,300 $ 11,600 Machine hours per unit 2.0 2.5 Machine hours used 495 Machine hours available 500 Quantity produced 115 115 Maximum demand 160 160 Profit $ 3,695 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

This question is related to the Key factor. Hence we need to understand first what is key factor?

• A key factor refers to the constraints ^{(restriction/scarce)} in availability of production resources.
• It is a factor which puts a limit on production and profit of a business.
• Key factor may be direct labor hours, raw materials shortage, demand of units, machine hours etc.
• In such a case, a decision has to be taken regarding the choice of the product whose production is to be increased, reduced or stopped.
• In key factor problems, selection of product is based on highest Contribution Margin per unit of limiting factor”.
• The product having highest contribution margin per unit of limiting factor should be given preference first and then second highest and so on.

In the given question the key factor is Machine Hours. Monthly Capacity of Machine = 500 Machine Hours

So we need to find out the Contribution Margin Per Unit Per Machine Hours.

Part 1 – Contribution Margin per unit per machine hour

1) Contribution Margin Per Unit Per Machine Hour
	Alpha	Deltas
Contribution Margin per unit (given)	$68.00	$65.00
Machine Hours needed per unit (b)	2 hours	2.5 hour
Contribution Margin per unit per machine hour (a/b)	$34.00	$26.00

Here, the contribution margin per unit per machine hour of Product “ALPHA” is higher, so the company should make the Alpha first because it provides higher contribution.

Total Available Machine Hours	500 Hours
Machine Hours Required to produce ALPHA (2 hours x 160 Units)	320 Hours
Total Available Hours for Production of Deltas	180 Hours
Maximum Delta Production (180 Hours / 2.5 Hours per unit needed)	72 Units

Part a --

The company should produce following quantity of Alphas and Deltas each month to maximize monthly profit

APLHA = 160 Units

DELTAs = 72 Units (as explained above)

Part b ----

To solve this part we need to calculate the Contribution Margin on the basis of Current Production Schedule and at the level of requirement a.

	Alpha	Deltas	Total
Current Level
Current Level of Production (A)	115 Units	115 Units
Contribution Margin Per Unit (B)	$68	$65
Total Contribution Margin at current level (A*B)	$7,820	$7,475	$15,295
At level found in requirement (A)
Optimal Production Level (P)	160 Units	72 Units
Contribution Margin Per Unit (C)	$68	$65
Total Contribution Margin at optimal level (P*C)	$10,880	$4,680	$15,560
Monthly profit increase over the current production schedule (15,560 - 15,295)			$265

Monthly Profit increase over the current production schedule is $265

Note ---- Fixed Cost is not considered in decision making since fixed cost will continue to incur whether company production ALpha or Delta.. It does not play any role in decision making.