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Smyrna industry is a firm that produces two products, Product A and Product B, in a single factory. The process to produce these two products are similar and the same two machines are being used, however the time required at each machine differs between products A and B. The two machines have different setup times and therefore total available monthly working hours differ.

Product A and Product B use the same raw material.

The available time in machines and labour, and total available units in raw material is shown in the table below.

Availability

Cost

Machine 1

130 hrs

$1 per hour

Machine 2

120 hrs

$1.5 per hour

Labour

200 hrs

$10 per hour

Raw Material

100 units

$5 per unit

Product A is processed in Machine 1 for 3 hours, and then moves to Machine 2 and is processed there for 2 hours.

Product B takes shorter in Machine 1, only 1 hour. However in Machine 2, Product 2 takes 3.5 hours.

Each hour of labour costs $10, each hour of work in Machine 1 costs $1, Machine 2 costs $1.50. Each unit of raw material costs $5.

Product A is sold for $70 and Product B is sold for $55. Their usage of material and hours is shown in the table.

Time in Machine 1, hours

Time in Machine 2, hours

Required Labour, hours

Raw Material, units

Selling Price, $

Product A

3

2

5

2

70

Product B

1

3.5

4

1

55

1. Formulate an LP model that determines the production plan such that Smyrna Industries attain the highest possible profit. Solve your model using Excel Solver. Generate the sensitivity report.

In the following questions, if Sensitivity Report is useful to answer, refer to the report and Sensitivity Analysis. Otherwise, find the new solution of optimization problem.

2. There is a possible modification in Machine 2. If that modification is done, the hourly cost of operating Machine 2 would go down to $1.30/hour. This modification costs $15 dollars. Should Smyrna Industries purchase this modification?

3. There is a possible modification in Machine 1. If that modification is done, the hourly cost of operating Machine 1 would go down to $0.70/hour. This modification costs $20 dollars. Should Smyrna Industries purchase this modification?

4. There is a new product, Product C, that Smyrna Industries can produce. If produced, Product C would be priced at $175. Product C uses 5 hours of production time in Machine 1 and Machine 2 each, and 10 hours of labour. It requires 10 units of raw material to be used in production. Considering that the costs are as in the initial question(the modifications in part 2 and 3 are not taken), should Smyrna Industries produce this new product? (don't re-solve the LP)

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