Nanuq Catering is planning to produce 'ready-to-go" tray of sandwiches. Each tray will include tuna, tuna/cucumber, ham, ham/cucumber, and cucumber sandwiches. Most popular orders come in the range of 100 to 120 sandwiches per tray. The management has specified a minimum of 15 each of tuna and ham and 25 each of tuna/cucumber and ham/cucumber sandwiches to be included in each tray. The company makes trays of sandwiches using the following resources: bread, tuna, ham, cucumber, mayonnaise, lettuce, and labour hours according to the plan shown in Table 1. The company has no shortage of bread. For each resource, the availability limit is listed in the last column of Table 1. Nanuq Catering is looking for the most economical combination of the tuna X, tuna/cucumber X2, ham X21, ham/cucumber X2 and cucumber X33 sandwiches to minimise the production cost per tray. The Excel sensitivity report is provided further below. Tuna (kg) Ham (kg) Cucumber (kg) Lettuce (kg) Table 1. The sandwich-making plan and availability of resources. Tuna Ham 0.15 0.20 Mayonnaise (kg) 0.04 Labour hours 0.22 Tuna/ Cucumber 0.10 0.15 0.10 0.03 0.25 0.20 0.20 0.04 0.22 Ham/ Cucumber Cucumber 0.10 0.15 0.10. 0.03 0.25 0.45 0.40 0.06 0.22 Availability 6.25 5.5 12 18 6 23.5 Question 1 continued The Excel Sensitivity Report: Adjustable Cells Cell $B$8 X 11 $C$8 X 12 $D$8 X 21 $E$8 X 22 $F$8 X 33 Constraints Name Cell Name $C$16 2 constraints Value $C$17 Value $C$18 Value $C$19 Value $C$20 Value $C$21 "s constraints Value. $C$22 Value $C$23 Value $C$24 Value $C$25 Value $C$26 Value $C$27 Value Final Value 25 25 15 25 10 Final Shadow Value Price 25 15 25 25 100 6.25 5.5 12 17 Reduced Cost 3.7 23.5 100 0 0 0 0 0 0 0.4 0.7 0.6 6.8 0 0 -0.7 0 0 0 0 Objective Allowable Allowable Coefficient ($) Increase Decrease 6.8 7.4 0.4 1E+30 7.2 1E+30 7,3 1E+30 6.5 0.3 15 15 25 25 100 6.25 5.5 12 18 6 23.5 120 Constraint Allowable Allowable R.H. Side Increase Decrease 10 0 0 0 0 0.3 0.7 1E+30 1E+30 2.25 1E+30 1E+30 1E+30 1E+30 500 0.4 460 0.6 0 0 6 0 10 0 0 0 1 2.3 0 20 (1) Write down the objective function of the linear programming problem. (2) Obtain the optimal value of the objective function. Nanuq Catering is expecting the cost of making a cucumber sandwich will increase by 30 cents. (3) What effect will this have on the objective function and optimal solution? (4) What is the shadow price for cucumber? Interpret the shadow price for cucumber. (5) If Nanuq Catering purchases 3 more kilograms of cucumber, what impact will this have on the optimal solution? Explain. Nanuq Catering has been offered 200-gram jars of sun-dried tomatoes at the same price as similar jars of mayonnaise. The company's management has worked out that they can accept the offer of one kilogram of sun-dried tomatoes to be included with ham sandwiches without attracting any extra cost to the company's current sandwich-making plan. (6) Explain how this could be done. 3