Product Mix Decision, Single and Multiple Constraints

Patz Company produces two industrial cleansers that use the same liquid chemical input: Regular Strength and Heavy Duty. Regular Strength uses two quarts of the chemical for every unit produced, and Heavy Duty uses five quarts. Currently, Patz has 6,000 quarts of the material in inventory. All of the material is imported. For the coming year, Patz plans to import 6,000 quarts to produce 2,818 units of Regular Strength and 1,272 units of Heavy Duty. The detail of each products unit contribution margin is as follows:

	Regular Strength		Heavy Duty
Selling price	$81		$139
Less variable expenses:
Direct materials	(20)		(50)
Direct labor	(21)		(14)
Variable overhead	(10)		(15)
Contribution margin	$30		$60

Patz Company has received word that the source of the material has been shut down by embargo. Consequently, the company will not be able to import the 6,000 quarts it planned to use in the coming year's production. There is no other source of the material.

Required:

1. Compute the total contribution margin that the company would earn if it could import the 6,000 quarts of the material.

$fill in the blank 1

2. Determine the optimal usage of the company's inventory of 6,000 quarts of the material. If no material should be allocated to the production of a product, enter "0" as your answer.

Regular Strength	fill in the blank 2	units
Heavy Duty	fill in the blank 3	units

Compute the total contribution margin for the product mix that you recommend.

$fill in the blank 4

3. Assume that Regular Strength uses three direct labor hours for every unit produced and that Heavy Duty uses two hours. A total of 6,000 direct labor hours is available for the coming year.

a. Formulate the linear programming problem faced by Patz Company. To do so, you must derive mathematical expressions for the objective function and for the materials and labor constraints. If a value is zero, enter "0" as your answer.

Let X = number of Regular Strength produced

Let Y = number of Heavy Duty produced

Objective function:	Max Z	=	$fill in the blank 5 X	+	$fill in the blank 6 Y
Subject to:
Direct materials constraint:	fill in the blank 7 X	+	fill in the blank 8 Y		fill in the blank 9
Direct labor constraint:	fill in the blank 10 X	+	fill in the blank 11 Y		fill in the blank 12
			X		fill in the blank 13
			Y		fill in the blank 14

b. Select the graph that solves the linear programming problem using the graphical approach.

(Units are in hundreds)

a.		b.
c.		d.

Correct answer is

abcdd

.

c. Compute the total contribution margin produced by the optimal mix. In solving for "Y", carry out computations to one decimal place. Round your final answers for "X" and "Y" to the nearest whole unit.

$fill in the blank 16