Calen Company manufactures and sells three products in a factory of three departments. Both labor and machine time are applied to the products as they pass through each department. The nature of the machine processing and of the labor skills required in each department is such that neither machines nor labor can be switched from one department to another.

Calen's management is attempting to plan its production schedule for the next several months. The planning is complicated by the fact that labor shortages exist in the community and some machines will be down several months for repairs.

Following is information regarding available machine and labor time by department and the machine hours and direct labor hours required per unit of product. These data should be valid for at least the next six months.

	Department
Monthly Capacity	1	2	3
Labor hours available	3,700	4,500	2,750
Machine hours available	3,000	3,100	2,700

Product	Input per Unit Produced	1	2	3
401	Labor hours	2	3	3
	Machine hours	1	1	2
402	Labor hours	1	2
	Machine hours	1	1
403	Labor hours	2	2	2
	Machine hours	2	2	1

Calen believes that the monthly demand for the next six months will be as follows:

Product	Units Sold
401	500
402	400
403	1,000

Inventory levels will not be increased or decreased during the next six months. The unit cost and price data for each product are as follows:

	Product
		401		402		403
Unit costs:
Direct material		$7		$13		$17
Direct labor		66		38		51
Variable overhead		27		20		25
Fixed overhead		15		10		32
Variable selling		3		2		4
Total unit cost		$118		$83		$129
Unit selling price		$196		$123		$167

Required:

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1. Calculate the monthly requirement for machine hours and direct labor hours for producing Products 401, 402, and 403.

	Labor hours	Machine hours
Product 401	fill in the blank 2d1ca3093fd5026_1	fill in the blank 2d1ca3093fd5026_2
Product 402	fill in the blank 2d1ca3093fd5026_3	fill in the blank 2d1ca3093fd5026_4
Product 403	fill in the blank 2d1ca3093fd5026_5	fill in the blank 2d1ca3093fd5026_6
Total	fill in the blank 2d1ca3093fd5026_7	fill in the blank 2d1ca3093fd5026_8

Which departments can meet the monthly sales demand?

All departmentsAll departments except for department 1All departments except for department 2All departments except for department 3Only Department 1Only Department 2Only Department 3All departments except for department 3

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Use monthly demand and input per unit produced. Are there any circumstances where hours needed exceed available hours?

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2. Determine the quantities of 401, 402, and 403 that should be produced monthly to maximize profits. Prepare a schedule that shows the contribution to profits of your product mix.

Calen Company Product Mix and Contribution Margin

Product	Number of Units	Contribution to profits
Product 401	fill in the blank b7f473fdcfaf078_1	$fill in the blank b7f473fdcfaf078_2
Product 402	fill in the blank b7f473fdcfaf078_3	fill in the blank b7f473fdcfaf078_4
Product 403	fill in the blank b7f473fdcfaf078_5	fill in the blank b7f473fdcfaf078_6
Total contribution margin		$fill in the blank b7f473fdcfaf078_7

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What is the contribution margin per unit of scarce resource?

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3. Assume that the machine hours available in Department 3 are 1,500 instead of 2,700. Calculate the optimal monthly product mix using the graphing approach to linear programming.

Corner Point	Optimal Monthly Product Mix
A	$ fill in the blank 15c475fa3fd8037_1
B	$ fill in the blank 15c475fa3fd8037_2
C	$ fill in the blank 15c475fa3fd8037_3
D	$ fill in the blank 15c475fa3fd8037_4
E	$ fill in the blank 15c475fa3fd8037_5

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Prepare a schedule that shows the contribution to profits from this optimal mix. (CMA adapted)

Calen Company Contribution to Profits from Optimal Sales Mix

Product	Contribution to Profits
Product 401	$fill in the blank 9915da0e501ef9b_1
Product 402	fill in the blank 9915da0e501ef9b_2
Product 403	fill in the blank 9915da0e501ef9b_3
Total contribution to profits	$fill in the blank 9915da0e501ef9b_4