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#### Q5) The Miramichi Furniture Manufacturer Co

###### Operations Management

Q5) The Miramichi Furniture Manufacturer Co. in Miramichi, N.B. produces two style types of tables (county contemporary) using three types of machines. The time required to produce the tables on each machine given in the following table.

 Machine Country Contemporary Total Machine Time Available per week Router 1.5 2.0 1000 Sander 3.0 4.5 2000 Polisher 2.5 1.5 1500

Country tables sell for \$350 and contemporary tables sell for \$450. Sales management has determined that at least 20% of the tables should be Country style and at least 30% should be Contemporary style.

How many of each type of tables should the company produce if it wants to maximize sales revenue?

a. Formulate an LP model for this problem.

b. Create an Excel spreadsheet model for this problem and solve using Solver.

c. What is the optimal solution?

d. Remove the integer constraint on the variable and use Solver to show how your spreadsheet model will differ if there are 25 types of tables and 15 machine processes involved in manufacturing them?

USE SOLVER TO CREATE A SENSITIVITY REPORT AND ANSWER THE FOLLOWING QUESTIONS

e. Remove the integer constraint on the variable. If the company could now get 50 more units of routing capacity, should they do it? If so, how much should they be willing to pay for it?

f. Remove the integer constraint on the variable. If the company could now get 50 more units of sanding capacity, should they do it? If so, how much should they be willing to pay for it?

g. Suppose the polishing time on country tables could be reduced from 2.5 to 2 units per table.

How much should the company be willing to pay to achieve this improvement In efficiency?

h. Contemporary tables sell for \$450. By how much would the sales price have to decrease before the company would no longer be willing to produce contemporary tables? Does this make sense? Explain briefly.

Q6. Antigonish Restaurant Is open from 8:00 am to 10:00 pm dally. Besides the hours the restaurant is open for customers, workers are needed an hour before opening and an hour after closing for set up and cleanup activities. The restaurant operates with both full-time and part-time workers on the following shifts:

 Shift Daily Pay Rate 7:00 am – 11:00 am \$32 7:00 am – 3:00 pm \$80 11:00 am – 3:00 pm \$32 11:00 am – 7:00 pm \$80 3:00 pm – 7:00 pm \$32 3:00 am – 11:00 pm \$80 7:00 pm – 11:00 pm \$32

The following numbers of workers are needed during each of the indicated time blocks.

 Hours Worked Needed 7:00 am – 11:00 am 11 11:00 am – 1:00 pm 24 1:00 pm – 3:00 pm 16 3:00 pm – 5:00 pm 10 5:00 pm – 7:00 pm 22 7:00 pm – 9:00 pm 17 9:00 pm – 11:00 pm 6

At least one full-time worker must be available during the hour before opening and after closing.

Additionally, at least 30% of the employees should be full-time (8 hour) workers during the restaurant's periods from 11:00 am = 1:00 pm and from 5:00 pm - 7:00 pm

a. Formulate and LP for this problem with the objective of minimizing total daily labor costs.

b. Implement your model in an Excel spreadsheet and use Solver to salve it.

What is the optimal solution?

Q7. A company produces three products which must be painted, assembled, and inspected.

The machinery must be cleaned and adjusted before each batch is produced. They want to maximize their profits for the amount of operating time they have. The unit profit and setup cost per batch are:

 Product Profit per unit Setup Cost per batch 1 9 500 2 10 600 3 12 650

The operation time per unit and total operating hours available are:

 Operating Time per Unit Operating Hours Available Operation Product 1 Product 2 Product 3 Paint 1 2 2 400 Assemble 2 3 2 600 Inspection 2 4 3 540

Formulate and solve a LP model for this problem with Solver.