(34 marks) A burger store sells two types of burgers: chicken burger and beef burger. Assume that
the input for the two types of burgers can be viewed in terms of just four resources: bread, cheese,
meat and labor.
The production of the two types of burgers in terms of these inputs is shown in the table below,
along with the unit selling prices of the burgers.
Bread (pieces)
Cheese (slices)
Chicken (Ibs)
Beef (Ibs)
Cooking (hours)
Selling price
Chicken Burger
2
2
0.5
Beef Burger
2
1.5
0.3
$33
0.4
0.4
$36.5
Resources Available
400
300
50
40
70
Bread can be obtained at $2 per piece, cheese can be obtained at $3 per slice, chicken can be
obtained at $20 per lbs and beef costs $30 per lbs. The cooking time costs $10 per hour. Each
resource is available in limited quantities as shown in the above table.
Assume the demand always exceeds the production capacities. The store owner would like to know
how to decide on the production plan that maximizes the profit. Answer the following questions:
a.
(4 marks) Write down the linear program to determine the optimal production plan.
- Ouestion 2 34 Marks A Burger Store Sells Two Types Of Burgers Chicken Burger And Beef Burger Assume That The Input F 1 (62.64 KiB) Viewed 22 times
- Ouestion 2 34 Marks A Burger Store Sells Two Types Of Burgers Chicken Burger And Beef Burger Assume That The Input F 2 (46.53 KiB) Viewed 22 times
- Ouestion 2 34 Marks A Burger Store Sells Two Types Of Burgers Chicken Burger And Beef Burger Assume That The Input F 3 (52.32 KiB) Viewed 22 times
Let X, and X, indicate the quantities of chicken and beef burgers, and the sensitivity report of the spreadsheet result is attached as below: Variable Cells Coll $B$4 $C$4 Name Chicken Burger (x1) Beef Burger (X2) Final Value 75 100 Reduced Objective Cost Coofficient 0 10 0 12 Allowable Increase 6 1E+30 Allowable Decrease 10 4.5 Constraints Cell Name $D$9 Bread LHS $D$10 Cheese LHS $D$11 Chicken LHS $D$12 Beef LHS $D$13 Cooking LHS Final Value 350 300 37.5 40 62.5 Shadow Price 0 5 0 11.25 0 Constraint R.H. Side 400 300 50 40 70 Allowable Increase 1E+30 50 1E+30 17.14285714 1E+30 Allowable Decrease 50 150 12.5 13.33333333 7.5 b. (2 marks) What is the optimal production plan and the optimal profit?
b. (2 marks) What is the optimal production plan and the optimal profit? c. (4 marks) What is the impact on total profit if the store has increased availability of beef by 10 lbs (to a total of 50 lbs)? d. (4 marks) Do you detect the existence of multiple optimal solutions? e. (6 marks) Suppose there is another cheese supplier who can provide additional 20 slices of cheese at the same unit cost, but would cost another $50 as transportation fee, should the store purchase these additional cheese? f. (4 marks)Suppose the selling price of chicken burger increases to $35. Show how you can compute the new optimal profit using the sensitivity report, or explain why you cannot determine the new optimal profit. g. (10 marks) Due to an adverse supply shock to the economy, prices of all resources (including bread, cheese, meat and labor) for the burger store are increased by 5% compared to the original value. Show how you can compute the new optimal profit using the sensitivity report, or explain why you cannot determine the new optimal profit.