Fundamentals of Cost Accounting 3rd Edition by William N. Lanen, Shannon W. Anderson, Michael Maher

Exercise 58

Optimum Product Mix—Excel Solver

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 150 units (each) monthly. Slavin is currently producing 110 Alphas and 110 Deltas each month. Cost and machine-usage data for the two products is shown in the following spreadsheet, which Slavin managers use for planning purposes:

	A	B	C	D	E	F	G	H
1			Alpha			Delta
2	Price		$ 120			$ 150
3	Less variable costs per unit
4	Material		20			35
5	Labor		26			37
6	Overhead		14			14
7	Contribution margin per unit		$ 60			$ 64
8
9	Fixed costs							Total
10	Manufacturing							$ 8,000
11	Marketing and administrative							$ 5,000
12								$ 13,000
13	Machine hours per unit		2.0			2.5
14
15
16	Machine hours used							495
17	Machine hours available							500
18
19	Quantity produced		110			110
20	Maximum demand		150			150
21	Profit		$ 640
22

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?

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

Step 1 of 2

Finding optimum product mix arises when there are scarce resources in the plant. In other words any material or time or any other resource is constraint than management thinks to maximize profits with limited resources available. For this situation, optimum product mix should be determined. In the present case, machine hours are the scarce resources and therefore, optimum product mix would be computed as follows.

a.

Determine the optimal production schedule for S corporation:

Details	Alpha	Delta	Total
Selling price per unit	$ 120.00	$ 150.00
Less: variable cost per unit
Material	$ 20.00	$ 35.00
Labor	$ 26.00	$ 37.00
Overhead	$ 14.00	$ 14.00
Variable cost per unit	$ 60.00	$ 86.00
Contribution margin per unit (A)	$ 60.00	$ 64.00
Fixed costs:
Manufacturing			$ 8,000
Marketing and administrative			$ 5,000
			$ 13,000
Machine hour required for 1 unit (B)	2	2.5
Contribution per machine hour (A) / (B)	$ 30.00	$ 25.60
Machine hours used			500
Machine hours available			500
Quantity Note 1	150	80
Profit Note 1	$ 1,120

Contribution margin per unit of scarce resource for Alpha and Delta are $30 and $25.60 respectively.

^{Note 1}

Details	Available hours except (D)
Total available machine hours (A)	500
Number of hours needed to produce Alpha units(150 units × 2 hours) (B)	300
Available hours used to produce Delta(200 hours / 2.5 hours)= 80 units (C)	200
Number Delta units that can be produced with available hours(200 hours / 2.5 hours) (D)	80 units