Product Mix Decisions, Multiple Constraints

Rahimi Company produces two types of gears: Model 12 and Model 15. Market conditions limit the number of each gear that can be sold. For Model 12 no more than 15,000 units can be sold, and for Model 15 no more than 40,000 units. Each gear must be notched by a special machine. Rahimi owns eight machines that together provide 60,000 hours of machine time per year. Each unit of Model 12 requires three hours of machine time, and each unit of Model 15 requires 45 minutes or 0.75 hour of machine time. The unit contribution for Model 12 is $60 and for Model 15 is $30. Rahimi wants to identify the product mix that will maximize total contribution margin.

Required:

1. Formulate Rahimi's problem as a linear programming model. If a value is zero, enter "0" as your answer.

Let X = Model 12 and Y = Model 15.

Max Z = $fill in the blank 1 X + $fill in the blank 2 Y

Subject to:

Constraint (1)	fill in the blank 3 X + fill in the blank 4 Y fill in the blank 5
Constraint (2)	X fill in the blank 6
Constraint (3)	Y fill in the blank 7
	X fill in the blank 8
	Y fill in the blank 9

2. Solve the linear programming model in Requirement 1. If a value is zero, enter "0" as your answer. Enter the units and the amounts in thousands (for example, "10,000" should be entered as "10").

(Units are in thousands)

	X-Value	Y-Value	Contribution Margin
Corner Point	(in thousands)	(in thousands)	(in thousands)
A	fill in the blank 10	fill in the blank 11	$fill in the blank 12
B	fill in the blank 13	fill in the blank 14	$fill in the blank 15
C	fill in the blank 16	fill in the blank 17	$fill in the blank 18
D	fill in the blank 19	fill in the blank 20	$fill in the blank 21
E	fill in the blank 22	fill in the blank 23	$fill in the blank 24

3. Identify which constraints are binding.