Dog Daze Manufacturing produces a variety of dog food products. These are made in batches and then kept in inventory that is used to fill orders from kennels and pet stores. The manager has helped to develop a linear programming model of the process for the company's three raw material input; X1, X2, X3:

X1 = bags of raw material 1

X2 = bags of raw material 2

X3 = bags of raw material 3

Minimize cost = 38X1 + 19X2 + 60X3,

Subject to

Protein: 2.5X1 + 4X2 + 3X3 794 pounds

Fiber: 3X1 + 2X2 + 4X3 300 pounds

Fat: 2X1 + X2 + 2X3 600 pounds

X1, X2, X3 0,

The manager has obtained the Excel output of sensitivity analysis for the model. The results are summarized in the answers and sensitivity reports given in the following table:

	A. Answer Report
	Target Cell (Min)
	Cell	Name	Original Value	Final Value
	$E$5	Cost Total	0	11400
	Adjustable Cells
	Cell	Name	Original Value	Final Value
	$B$4	Quantities Raw Material 1	0	292
	$C$4	Quantities Raw Material 2	0	16
	$D$4	Quantities Raw Material 3	0	0
	Constraints
	Cell	Name	Cell Value	Formula	Status	Slack
	$E$7	Protein Constraint Usage	794	$E$7>=$F$7	Binding	0
	$E$8	Fiber Constraint Usage	908	$E$8>=$F$8	Not Binding	608
	$E$9	Fat Constraint Usage	600	$E$9>=$F$9	Binding	0
	$B$4	Quantities Raw Material 1	292	$B$4>=0	Not Binding	292
	$C$4	Quantities Raw Material 2	16	$C$4>=0	Not Binding	16
	$D$4	Quantities Raw Material 3	0	$D$4>=0	Binding	0
	B. Sensitivity Analysis
	Adjustable Cells
			Final	Reduced	Objective	Allowable	Allowable
	Cell	Name	Value	Cost	Coefficient	Increase	Decrease
	$D$5	Quantities Raw Material 1	292	0	38	0	26.125
	$D$6	Quantities Raw Material 2	16	0	19	41.8	0
	$D$7	Quantities Raw Material 3	0	22	60	1E+30	22
	Constraints
			Final	Shadow	Constraint	Allowable	Allowable
	Cell	Name	Value	Price	R.H. Side	Increase	Decrease
	$E$7	Protein Constraint Usage	794	0	794	1606	44
	$E$8	Fiber Constraint Usage	908	0	300	608	1E+30
	$E$9	Fat Constraint Usage	600	19	600	35.2	401.5

Use above table to answer the followingquestions about the model:

1. Which constraints are binding on the solution? How do you know? (3)
2. What does the reduced cost of 22 indicates? (3)
3. How do you interpret the 608 in the allowable increase section of the fiber constraint?

(2)

1. Determine the range of optimality for the objective function coefficients of X1 and X2.

(4)

1. What does the shadow price of 19 reveal? (4)
2. What is the range of feasibility for the fat constraint's RHS? (3)
3. Would a decrease to 575 for the RHS of the fat constraint affect the optimal value of the objective function? If so, by how much? (3)
4. The manager is considering reducing each RHS by 9 percent and may ask you to provide information on how that would impact the total cost. If you are asked, what would you need to do? Why? (3)