Question: Wacco produces 2 products: 1 and 2. The relevant data are shown in the table below:

Each week, up to 400 units of raw material can be purchased at a cost of $1.50 per unit. The company employs 4 workers, who work 40 hours per week (their salaries are considered a fixed cost). Worker can be asked to work overtime and are paid $6/hour for overtime work. Each week, 320 hours of machine time are available.

In the absence of advertising, 50 units of product 1 and 60 units of product 2 will be demanded each week. Advertising can be used to stimulate demand for each product. Each dollar spent on advertising product 1 increases its demand by 10 units; each dollar spent on advertising product 2 increases its demand by 15 units. At most $100 can be spent on advertising. Define:

P1 = the number of units of product 1 produced each week

P2 = the number of units of product 1 produced each week OT = the number of hours of overtime labor used each week RM = the number of units of raw material purchased each week

A1 = dollars spent each week advertising product 1

A2 = dollars spent each week advertising product 2

Use these variable definitions to formulate an LP that will maximize Wacco ^' s profit. Use the output to answer the following questions:

1. If overtime were only $4/ hour, would Wacco use it?
2. If each unit of product 1 sold for $15.50, would the current basis remain optimal? What would be the new optimal solution?
3. What is the most that Wacco should be willing to pay for another unit of raw material?
4. How much would Wacco be willing to pay for another hour of machine time?
5. If each worker were required to work 45 hours per week (as part of their

regular workweek … not as 5 hours of overtime), what would the company ^' s

profit be?

Please enter the answer to part b - what is the profit if this change is made?

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