Question

Problem 4-64 Optimum Product Mix-Excel Solver (LO 4-4)

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 170 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		$	155
Less variable costs per unit
Material		17			32
Labor		23			35
Overhead		14			14
Contribution margin per unit	$	71		$	74
Fixed costs
Manufacturing							$	7,400
Marketing and administrative							$	4,400
							$	11,800
Machine hours per unit		2.0			2.5
Machine hours used								495
Machine hours available								500
Quantity produced		115			115
Maximum demand		170			170
Profit	$	4,875

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

Part A )

Total capacity of Machine = 500 hours

Machine hours requied = 765 hours ( 170*2 + 170*2.5 )

Capacity is less than demand of machine hours, therefore machine hour is limiting factor.

We should produce goods based on ranking of contribution per limiting factor.

Calculation of Contribution per Limiting Factor

	Alpha	Beta
Contribution per unit	71	74
Machine hours required	2	2.5
Contribution per limiting factor	35.5	29.6
Ranking	I	II

Allocation of products based on ranking

Product	Units	Machine hours per unit	Machine hours used	Cumulative machine hours
Alpha	170	2 hrs	340 hrs	340 hrs
Beta	64	2.5 hrs	160 hrs (500-340)	500 hrs

Therefore optimum production units are 170 of Alpha and 64 units of Beta

Part B

Particulars	Calculation	Amount ( $ )
Contribution as per optimum production
* Alpha	170*71	12070
* Beta	64*74	4736
		16806
Less : Fixed Cost
* Manufacturing	given	7400
* Marketing and administrative	given	4400
		11800
Profit as per optimum prodution	16806-11800	5006
Profit as per current production	given	4875
Difference		131

Increase in profit will be $ 131.