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[answered] ASSIGNMENT 3 PART 1. Natural Furniture Company manufactures


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Formulate as a Linear Programming problem to maximize profit.


ASSIGNMENT 3 PART 1. Natural Furniture Company manufactures three outdoor products, chairs, benches, and tables.

 

Each product must pass through the following departments before it is shipped: sawing, sanding,

 

assembly, and painting. The time requirements (in hours) are summarized in the tables below.

 

The production time available in each department each week and the minimum weekly production

 

requirement to fulfill contracts are as follows: Departmen

 

t

 

Sawing

 

Sanding

 

Assembly

 

Painting

 

Product

 

Chairs

 

Benches

 

TABLES Capacity

 

(In Hours)

 

450

 

400

 

625

 

550 Sawing

 

1.5

 

1.5

 

2.0 Product

 

Chairs

 

Benches

 

Tables Sanding

 

1.0

 

1.5

 

2.0 Minimum

 

Production

 

Level

 

100

 

50

 

50 Assembly

 

2.0

 

2.0

 

2.5 Paintin

 

g

 

1.5

 

2.0

 

2.0 Profit

 

$15

 

$10

 

$20 The production manager has the responsibility of specifying production levels for each product for the

 

coming week. Formulate as a linear programming problem to maximize profit.

 

What mix of products would yield maximum profit?

 

Solve with computer software. Show computer output. The production manager has the responsibility of specifying production

 

levels for each product for the coming week. Let

 

X1_ Number of chairs produced

 

X2_ Number of benches produced

 

X3_ Number of tables produced

 

The objective function is

 

Maximize profit _ 15X1 _ 10X2 _ 20X3

 

Constraints

 

1.5X1 _ 1.5X2 _ 2.0X3 _ 450 hours of sawing available

 

1.0X1 _ 1.5X2 _ 2.0X3 _ 400 hours of sanding available

 

2.0X1 _ 2.0X2 _ 2.5X3 _ 625 hours of assembly available

 

1.5X1 _ 2.0X2 _ 2.0X3 _ 550 hours of painting available

 

X1 _ 2.0X2 _ 2.0X3 _ 100 chairs

 

X2 _ 2.0X3 _ 50 benches

 

X3 _ 50 tables

 

X1, X2, X3 _ 0 Page 1 of 2-Quantitative Methods in Business & Management PART 2. A phosphate manufacturer produces three grades of phosphate, A, B, and C, which yield profit

 

of $40, $50, and $60 per kilogram, respectively. The products require the labor and materials per batch

 

that are shown in the table. Each batch of Grade A phosphate yields 800kg of phosphate; each batch of

 

Grade B phosphate yields 700kg of phosphate; and each batch of Grade C phosphate yields 800kg of

 

phosphate. Labor hours

 

Raw material #1

 

Raw material #2 Grade

 

A

 

4

 

200

 

600 Grade

 

B

 

4

 

300

 

400 Grade

 

C

 

5

 

300

 

500 Available

 

Resources

 

80 hr

 

6,000 kg

 

5,000 kg Formulate as a Linear Programming problem to maximize profit.

 

What mix of products would yield maximize profit? _________________________

 

Solve this with computer software to show the solution.

 

Minimize cost _ 40A _ 50B _ 60C

 

Constraints

 

Labor: 4A _ 4B _ 5C _ 80

 

Raw material #1 200A _ 300B _300C _ 6,000

 

Raw material #2 600A _ 400B _500C _ 5,000 Page 2 of 2-Quantitative Methods in Business & Management

 


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