3 a. Solve the following Linear programming problem and obtain sensitivity analysis. 2 SABA toy manufacturers make four different types of stuffed animals. The 3 following LP model has been developed for the company. 4 5 Let X1 - Number of stuffed bears 6 X2 - Number of stuffed rabbits 7 X3 = Number of stuffed dogs X4 = Number of stuffed cats 9 0 The LP Model PRODUCTS X1 X2 X3 X4 Available RESOURCES 12 Constraint 1 3 1 1 1 100 Stuffing in pounds 13 Constraint 2 2 2 3 2 250 Yards of fabric 14 Constraint 3 5 3 1 2 300 Assembly time in hours 15 Constraint 4 1 4 3 200 Pieces of trim 16 Profit/unit 8.00 S 5.00 $ 6,00 S 4.00 17 CE E F G H I J K L Problem 1 parts b, c, d, and e - Use your sensitivity output to answer the following questions. 5 b. Which constraints are(is) non-binding and what does it mean? 5 5 7 Bc. If the profit per unit of stuffed rabbits is increased by S2, will the optimal solution change? What would be the new value of the objective function? Give the new value here 0 1 2 3 6 4 d. As you note, at optimum no stuffed cats (X4) are being produces $ What should the profit per unit of stuffed cats (X4), so it becomes profitable to produce it? Explain how you arrived at the value) 7 8 9 20 e. Fifty yards of fabric can be obtained at 1.20 above the current cost. 21 Should the additional yards of fabric be obtained at the quoted cost? Why or why not? Fully explain. 22 23 34