Solve the below problem:
Q: The manager of a Burger Doodle franchise wants to determine how many sausage biscuits and ham biscuits to prepare each morning for breakfast customers. The two types of biscuits require the following resources:
| Biscuit |
Labor (hr.) |
Sausage (lb.) |
Ham (lb.) |
Flour (lb.) |
| Sausage |
0.010 |
0.10 |
--- |
0.04 |
| Ham |
0.024 |
--- |
0.15 |
0.04 |
The franchise has 6 hours of labor available each morning. The manager has a contract with a local grocer for 30 pounds of sausage and 30 pounds of ham each morning. The manager also purchases 16 pounds of flour. The profit for a sausage biscuit is $0.60; the profit for a ham biscuit is $0.50. The manager developed a mathematical model and solved it using excel solver. Answer the following questions based on the excel solver sensitivity report below.
Variable Cells
| Name |
Final Value |
Reduced Cost |
Objective Coefficient |
Allowable Increase |
Allowable Decrease |
| Sausage Biscuits |
300 |
0 |
0.6 |
1E+30 |
0.1 |
| Ham Biscuits |
100 |
0 |
0.5 |
0.1 |
0.5 |
Constraints
| Name |
Final Value |
Shadow Price |
Constraint R.H. Side |
Allowable Increase |
Allowable Decrease |
| Labor Usage (hr/unit) |
5.4 |
0 |
6 |
1E+30 |
0.6 |
| Sausage Usage (lb/unit) |
30 |
1 |
30 |
10 |
4.285714286 |
| Ham Usage (lb/unit) |
15 |
0 |
30 |
1E+30 |
15 |
| Flour Usage (lb/unit) |
16 |
12.5 |
16 |
1 |
4 |
a) Formulate a linear programming model for this problem.
Show the related cells in the excel report for answering the following questions:
b) What would be the change in the profit, if the available sausage increases to 35 pounds?
c) What is the range for the profit from Ham biscuit that keeps the current solution optimal?
d) How much extra sausage and ham is left over at the optimal solution point? Is there any idle labor time?
e) Will you consider buying additional Ham or Sausage as raw materials? If so, what will be prices (per lb) will you recommend buying Ham / Sausage?
f) What would be the effect on the optimal solution if the manager could obtain 2 more pounds of flour?
g) Given the prices of the resources reported by the excel solver and resources required to produce one sausage and ham biscuit, what is the total value of resources used to produce one sausage and one ham biscuit?
h) The manager wants to introduce a new biscuit which contains both sausage (0.10 lb) and ham (0.10 lb), and 0.020 labor hour and 0.04 lb of flour. The product is expected to provide a profit of $0.55 per biscuit. How many biscuits should he make?