Operations Homework 4
Due February 27
1 QuickCare Medical Center
QuickCare Medical Center is a hospital that staffs two different kinds of em- ployees: Doctors and Nurses. Each day, the facility must manage patient flow while staying within labor constraints. Each doctor can see 12 patients per shift and each nurse can see 8 patients per shift. Each doctor works 10 hours per shift and each nurse works 8 hours per shift. There are a maximum of 160 doctor-hours and a maximum of 240 nurse-hours to allocate per day. The combined number of doctors and nurses cannot exceed 40.
The clinic aims to maximize the number of patients treated over a given day.
1. Write the equations for the linear program that can be used to solve for the number of doctors and nurses in order to maximize the number of patients seen.
2. Graph the linear program below with the number of doctors on the x axis and the number of nurses on the y axis.
3. List the corner points and their corresponding objective values
4. What is the optimal allocation of doctors and nurses?
5. List which constraints are binding
6. Suppose now that the hospital is able to expand and can now staffa com- bined 50 doctors and nurses. How many patients can be seen per day?
2 Yean’s Bakery
Yean’s bakery sells three types of baked goods: Cakes, cupcakes, and muffins. Cakes sell for $12, cupcakes for $6, and muffins for $4. Each good requires sugar, flour and butter with the following requirements for each
|
Ingredient
|
Cake
|
Cupcake
|
Muffin
|
|
Sugar
|
5
|
3
|
2
|
|
Flour
|
2
|
2
|
4
|
|
Butter
|
0.5
|
0.25
|
0.15
|
Yean has 60 cups of sugar, 100 cups of flour and 5 cups of butter at his disposal.
1. What is the optimal number of cakes, cupcakes, and muffins that Yean should make? At this allocation, what is Yean’s revenue? Include the Excel screenshot as well as the sensitivity table.
2. Suppose Yean can now charge $13 for cakes. Does his optimal allocation of resources change? If so, what is his new allocation?
3. Suppose Yean is able to buy another cup of butter to use per day at a cost of $18. Should he do it? Why or why not?