### Formulate the problem levels as a linear program

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(THE QUESTION IS FROM PRODUCTION AND OPERATIONS ANALYSIS , 7TH EDITION, CHAPTER 3RD, 36TH PROBLEM)( THE PROBLEM IS MOSTLY SOLVED IN EXCEL)

The yeasty brewing company produces a popular local beer known as iron stomach. Beer sales are some what seasonal, and yeasty is planning its production and workforce levels on march 31st for the next six months. the demand forecasts are as follows:

month production days forecast demand (in hundreds of cases)

april 11days 85cases

may 22days 93cases

june 20days 122cases

july 23days 176cases

august 16days 140cases

sept 20days 63cases

As of march 31, yeasty had 86 workers on the payroll. over a period of 26 working days when there were 100 workers on the payroll, yeasty produced 12000 cases of beer. The cost to hire each worker is \$125 and cost of laying off each worker is \$300.Holding costs amount to 75 cents per case per month.

As of march 31, yeasty expects to have 4500 cases of beer in stiock, and it wants to maintain buffer inventory of 1000 cases each month. It plans to start october with 3000 cases on hand.

a) Based on the information find the minimum constant workforce plan for yeasty over the six months, and determining hiring, firing, and holding costs associated with that plan.

b) Suppose that it takes one month to train a new worker. How will that affect your solution?

c) Suppose that the maximum number of workers that the comapny can expect to be able to hire in one month is 10. How will it affect your solution in part (a)?

d) Formulate the problem levels as a linear program. ( you may ignore the conditions in parts (b) and (c))

e) Sove the resulting linear program. Round the appropriate variables and determine the cost ofyour solution.

f) Suppose yeasty doesnt not wish to fire any workers.What is the optimal plan subject to this constraint?

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