Submit your work as an excel file. You must show your work details to earn credit for this homework.

$1.$ Develop a workforce schedule $($using Linear Programming to model and solve this problem$)$

A local bank needs the minimum number of employees needed for each day of the week listed in the following table. If a staff is hired, his$/$her schedule will be working $5$ consecutive days and take two days off. The bank operates seven days a week.

Day of the Week M T W TH F Sa Su

Number of staff needed $4553523$

So how will you help the bank hire the staffs?

$2.$ You have been assigned responsibility for scheduling a new cell in the plant and are provided the following information:

a$)$ A factory has a dedicated cell that uses $5$ distinct resources.

b$)$ The resources are not interchangeable.

c$)$ The cell produces $2$ products: Model A and Model B$.$

d$)$ Continuing market demand for A$=25$ units and for B$=35$ units.

e$)$ Capacity per day for each resource is $960$ minutes, $7$ days$/$week$.$

f$)$ No overtime is allowed.

g$)$ Operating expenses regardless of product mix total $$1000/$day$.$

h$)$ Material cost for Model A $=$ $$10/$unit and for Model B $=$ $$10/$unit$.$

i$)$ Selling price for Model A $=$ $$45$ and for Model B $=$ $$50.$

j$)$ The process is given in the diagram to the right.

k$)$ No setups are required for either product.

Discuss the product mix that you would run and explain why. Make sure that you show and label all relevant calculations using Theory of Constraints thinking. Calculate the profit that this cell would make using your product mix.