2.1 Brown Furniture Revisited Revisit the Brown Furniture

2.1

Brown Furniture Revisited Revisit the Brown Furniture allocation example of this chapter. As plans are being made for a new quarter, a revised set of figures on resource availabilities is compiled. The new resource limits are as follows.

Fabrication hours

2000

Assembly hours

1800

Machining hours

1600

Wood supply

9400

The other data, on profit contributions and resource consumptions, all remain unchanged.

  1. What are the optimal production quantities of chairs, desks and tables?
  2. What is the maximum profit contribution?
  3. Which constraints are binding in the optimal solution?

2.6

Coffee Blending and Sales Hill-O-Beans Coffee Company blends four component beans into three final blends of coffee: one is sold to luxury hotels, another to restaurants, and the third to supermarkets for store-label brands. The company has four reliable bean supplies: Argentine Abundo, Peruvian Colmado, Brazilian Maximo, and Chilean Saboro. The table below summarizes the very precise recipes for the final coffee blends, the cost and availability information for the four components, and the wholesale price per pound of the final blends. The percentages indicate the fraction of each component to be used in each blend.

Open table as spreadsheet

Component (pounds)

Hotel

Rest

Market

Cost per pound

Max. weekly availability

Abundo

20%

35%

10%

$0.60

40,000

Colmado

40%

15%

35%

$0.80

25,000

Maximo

15%

20%

40%

$0.55

20,000

Saboro

25%

30%

15%

$0.70

45,000

Wholesale price per pound

$1.25

$1.50

$1.40

The processor's plant can handle no more than 100,000 lb per week, and Hill-O-Beans would like to operate at capacity, if possible. Selling the final blends is not a problem, although the Marketing Department requires minimum production levels of 10,000, 25,000, and 30,000 lb, respectively, for the hotel, restaurant and market blends.

  1. To maximize weekly profit, how many pounds of each component should be purchased?
  2. How would the optimal profit change if there were a 1000-lb increase in the availability of Abundo beans? Colmado? Maximo? Saboro?

2.14

Production Planning The Kim Camera Company produces four different camera models, known as C1–C4. Each model can be made by two different methods. The manual method requires work in the Fabrication, Assembly, and Test departments, while the automated method combines the Assembly and Test operations in one department. The first table below describes the price and cost features of the camera models, along with marketing information on the range of possible sales in the coming month. Because model C1 is delivered to one large retailer under a long-term contract, a threshold demand quantity of 1500 units must be met. For the other models, there is flexibility in how much demand to meet, up to a ceiling that represents maximum possible sales.

Open table as spreadsheet

C1

C2

C3

C4

Price

125

175

200

135

Manual cost

110

160

155

125

Auto cost

100

112

150

90

Manual margin

15

15

45

10

Auto margin

25

63

50

45

Sales max.

3000

2500

2000

3200

Sales min.

1500

0

0

0

The next table provides data on the various departments at the firm, consisting of the time per camera required in each department and the number of hours available in each department during the month.

Open table as spreadsheet

C1

C2

C3

C4

Hours

Manual fab.

3

5

4

4

16,000

Manual asy.

8

12

10

9

30,000

Manual test

2

3

5

2

15,000

Auto fab.

5

6

7

4

24,000

Auto asy/test

4

5

8

5

20,000

  1. What production plan will maximize profit for Kim Camera?
  2. How would the solution in(a)change if there were no threshold requirement for Camera C1?

Complete the following problems from the textbook:

Exercise 2.1: Brown Furniture Revisited (Please use the this link below - Chapter 2 to find a similar allocation model) http://faculty.tuck.dartmouth.edu/optimization-modeling/text-figures

Exercise 2.6: Coffee Blending and Sales (Your three decision variables are the three different Blends - Hotel, Restaurant, market)

Exercise 2.14: Production Planning (You need to have 8 decision variables representing 4 manuals and 4 automatics)

Set up the model and use Excel Solver to solve. Generate the Answer Report and include a brief interpretation for each problem. Complete your work in Excel