Formulate a linear programming model for the above situation by determining (a)

Question

Formulate a linear programming model for the above situation by determining (a) The decision variables. X1 = # of ham and cheese sandwiches to be made X2 = # grilled vegetables sandwiches to be made X 3 = # of chicken salad sandwiches to be made (b) Determine the objective function. What does it represent? Maximize profit Z = (0.6x1 + 0.55x2 + 0.70x3) It represents the total profit that is obtained by making xl, x2, and x3 the number of each type of sandwiches. (c) Determine all the constraints. Briefly describe what each constraint represents. 0.45x1+ 0.4x2 + 0.6x3 1920 the available time to make all of the sandwiches Xxx4000 Xi1000 Xix3x 20 the total number of sandwiches does not exceed past 4000 the company can make no more than 1000 ham and cheese sandwiche:s - Hint: There are 3 variables and 3 constraints (in addition to the non-negativity constraints) for this problem. 2. Find the computer solution, including the ranging (sensitivity analysis) results, for Question 1 by using QM for Windows or Excel. Determine the optimal solution (including the decision variables and the slack/surplus variables) and optimal profit. Interpret the optimal solution and optimal profit.

Explanation / Answer

X1 X2 X3 1000 1650 1350 0.6 0.55 0.7 2452.5 Constraint 1 0.45 0.4 0.6 1920

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