## [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 &amp; 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

A

4

200

B

4

300

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 &amp; Management

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