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

Exercise 59

Optimum Product Mix–Excel Solver

Layton Machining Company (LMC) manufactures two versions of a basic machine tool. One ver­sion is a standard model and one is a custom model, which requires some additional work and slightly higher-grade materials. The manufacturing process at LMC requires that each product go through two departments, Grinding and Finishing. The process in each department uses a single type of machine. Total machine capacity in Grinding is 50,000 hours, and in Finishing, total ma­chine capacity is 30,000 hours. (Each department has multiple machines.) Total market demand is limited to 100,000 standard units and 120,000 custom units monthly. LMC is currently producing 90,000 standard units and 50,000 custom units each month. Cost and machine-usage data for the two products follow:

	A	B	C	D	E	F	G	H
1			Standard			Custom
2	Price		$ 6.00			$ 8.00
3	Less variable costs per unit
4	Material		1.50			2.00
5	Labor		1.25			1.50
6	Overhead		1.75			2.50
7	Contribution margin per unit		$ 1.50			$ 2.00
8
9	Fixed costs							Total
10	Manufacturing							$ 76,000
11	Marketing and administrative							37,000
12								$ 113,000
13
14	Grinding machine hours per unit		0.2			0.3
15	Finishing machine hours per unit		0.1			0.4
16	Grinding machine hours used							33,000
17	Grinding machine hours available							50,000
18	Finishing machine hours used							29,000
19	Finishing machine hours available							30,000
20
21	Quantity produced		90,000			50,000
22	Maximum demand		100,000			120,000
23	Profit		$ 122,000

Required

a.What is the optimal production schedule for LMC? In other words, how many standard units and custom units should the company produce each month to maximize monthly profit?

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b.If LMC produces at the level found in requirement (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 LMC:

Details	Standard	Custom	Total
Selling price per unit	$ 6.00	$ 8.00
Less: variable cost per unit
Material	$ 1.50	$ 2.00
Labor	$ 1.25	$ 1.50
Overhead	$ 1.75	$ 2.50
Variable cost per unit	$ 4.50	$ 6.00
Contribution margin per unit (A)	$ 1.50	$ 2.00
Fixed costs:
Manufacturing			$ 76,000
Marketing and administrative			$ 37,000
			$ 113,000
Grinding machine hour required per unit (B)	0.2	0.3
Finishing machine hour required per unit (C)	0.1	0.4
Contribution per grinding machine hour (A) / (B)	$ 7.50	$ 6.67
Contribution per finishing machine hour (A) / (C)	$ 15.00	$ 5.00
Grinding machine hour used			35000
Grinding machine hours available			50,000
Finishing machine hour used			30,000
Finishing machine hours available			30,000
Quantity produced	100,000	50,000
Maximum demand	100,000	120,000
Profit			$ 137,000

Contribution margin per unit of scarce resource for Standard and Custom are $1.50 and $2.00 respectively.

^{Note 1}

Details	Grinding machine - Available hours except (D)	Finishing machine - Available hours except (D)
Total available machine hours (A)	50,000	30,000
Number of hours needed to produce Standard units(100,000units × 0. 2 hours) (B)(100,000 units × 0.1 hours)	20,000	10,000
Available hours used to produce Custom(15,000 hours / 0.3 hours)= 50,000 units (20,000 hours / 0.4 hours) = 50,000 units	15,000	20,000