Question: 2) The LP model below is developed to determine optimal number of product 1 (x1), product 2 (x2), product 3 (x3), and product 4 (x4)

2) The LP model below is developed to determine

2) The LP model below is developed to determine optimal number of product 1 (x1), product 2 (x2), product 3 (x3), and product 4 (x4) to stock at a Department Store so that sales revenue can be maximized. The coefficients of the objective function show selling price of each product (in $). Constraint 1 measures display space in units, constraint 2 measures time to set up the display in minutes. Note that product 3 (x3) does not require any time to make it ready for display. Constraints 3 and 4 are marketing restrictions. Constraint 3 indicates that the maximum demand for product 1 and product 3 is 25 units, while constraint 4 specifies that the total demand for second, third and fourth type of products is at least 50 units. (56 pts) Xi: The stock quantity of product i (i=1, 2, 3, 4) Max Z=100x1 + 120x2 + 150x3 + 125x4 subject to: xl + 2x2 + 2x3 + 2x4 50 (constraint 4: minimum demand) xl, x2, x3, x4 > 0 87.5 The computer solution to this model is given below. Answer the following "What If Questions": Variable Value Reduced Cost Original Val Lower Bound Upper Bound X1 8 0 0 100 Infinity X2 0 5 5 120 - Infinity 125 X3 17 0 0 150 125 162.5 X4 33 0 125 120 150 1 Constraint Dual Value Slack/Surplus Original Val Lower Bound Upper Bound Display Space in Units 75 0 108 100 123.75 Time to Set Up 0 63 120 57 Infinity Maximum Demand 25 0 25 8 8 58 Minimum Demand -25 0 50 41.5 54 a) What is the optimal solution? (write down the values of decision variables and the value of objective function)? (8 pts) b) How would the value of objective function change if the available display space is increased by 10 units? (8 pts) c) How would the value of objective function change if available time to set up the display is increased by 10 minutes? (8 pts) d) What would be the effect of increasing the selling price of the first product by $5 on optimal solution and on value of objective function? (8 pts) e) What would be the effect of decreasing the price of the third product by $10 on optimal solution and on value of objective function? (8 pts) f) Interpret the reduced cost" for second type of product (x2)(8 pts) g) What if the total minimuin demand for second, third and fourth type of products (constraint 1) were 40 units instead of 50 units? What would be the effect of this change on value of objective function? (8 pts)

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