Question

MAT540 Homework Week 6

Page 1 of 2

MAT540

Week 6 Homework

Chapter 2

1. A Cereal Company makes a cereal from several ingredients.
Two of the ingredients, oats and rice,

provide vitamins A and B. The company wants to know how many
ounces of oats and rice it should

include in each box of cereal to meet the minimum
requirements of 45 milligrams of vitamin A and

13 milligrams of vitamin B while minimizing cost. An ounce of
oats contributes 10 milligrams of

vitamin A and 2 milligram of vitamin B, whereas an ounce of
rice contributes 6 milligrams of A

and 3 milligrams of B. An ounce of oats costs $0.06, and an
ounce of rice costs $0.03.

a. Formulate a linear programming model for this problem.

b. Solve the model by using graphical analysis.

2. A Furniture Company produces chairs and tables from two
resources- labor and wood. The

company has 125 hours of labor and 45 board-ft. of wood
available each day. Demand for chairs is

limited to 5 per day. Each chair requires 7 hours of labor
and 3.5 board-ft. of wood, whereas a table

requires 14 hours of labor and 7 board-ft. of wood. The
profit derived from each chair is $325 and

from each table, $120. The company wants to determine the
number of chairs and tables to produce

each day in order to maximize profit. Formulate a linear
programming model for this problem.

a. Formulate a linear programming model for this problem.

b. Solve the model by using graphical analysis. (Do not round
the answers)

c. How much labor and wood will be unused if the optimal
numbers of chairs and tables are

produced?

3. Kroeger supermarket sells its own brand of canned peas as
well as several national brands. The

store makes a profit of $0.28 per can for its own peas and a
profit of $0.19 for any of the national

brands. The store has 6 square feet of shelf space available
for canned peas, and each can of peas

takes up 9 square inches of that space. Point-of-sale records
show that each week the store never

sales more than half as many cans of its own brand as it does
of the national brands. The store

wants to know how many cans of its own brand of peas of peas
and how many cans of the national

brands to stock each week on the allocated shelf space in
order to maximize profit.

a. Formulate a linear programming model for this problem.

b. Solve the model by using graphical analysis.

MAT540 Homework Week 6

Page 2 of 2 4. Solve the following linear programming model
graphically:

Minimize Z=8X1 + 6X2

Subject to

4X1 + 2X2 20

-6X1 + 4X2

X1 + X2

X1 , X2

P1

(a) Define the decision variables and write the linear programming model for the problem in the space provided below

(b) Sketch the feasible region. Give your answer in the worksheet named P1-Graph

(i) You can use QM for Windows to get the graph, copy and paste it onto the worksheet named P1-Graph OR

(ii) You can sketch the feasible region on paper, scan and save it in your computer.

Copy the image (i.e. graph) and paste it onto the worksheet named P1-Graph

(c’) Write all the vertices of the feasible region and identify the optimal vertex

What is the optimal objective function value?

Vertex

x1

x2

x1

x2

1

optimal vertex

2

3

optimal objective fuction value

P1-Graph

P2

(a) Define the decision variables and write the linear programming model for the problem in the space provided below

(b) Sketch the feasible region. Give your answer in the worksheet named P2-Graph

(i) You can use QM for Windows to get the graph, copy and paste it onto the worksheet named P2-Graph OR

(ii) You can sketch the feasible region on paper, scan and save it in your computer.

Copy the image (Graph) and paste it onto the worksheet named P2-Graph

Write all the vertices of the feasible region and identify the optimal vertex

What is the optimal objective function value?

Vertex

x1

x2

x1

x2

1

optimal vertex

2

3

optimal objective fuction value

4

5

(c’)

How much labor and wood will be unused if the optimal number
of chairs and tables are used?

Provide your answer in the space below

P2-Graph

P3

(a) Define the decision variables and write the linear programming model for the problem in the space provided below

(b) Sketch the feasible region. Give your answer in the worksheet named P4-Graph

(i) You can use QM for Windows to get the graph, copy and paste it onto the worksheet named P4-Graph OR

(ii) You can sketch the feasible region on paper, scan and save it in your computer.

Copy the image (Graph) and paste it onto the worksheet named P4-Graph

(c’) Write all the vertices of the feasible region and identify the optimal vertex

What is the optimal objective function value?

Vertex

x1

x2

x1

x2

1

optimal vertex

2

3

optimal objective fuction value

P3-Graph

P4

(a) Sketch the feasible region. Give your answer in the worksheet named P5-Graph

(i) You can use QM for Windows to get the graph, copy and paste it onto the worksheet named P5-Graph OR

(ii) You can sketch the feasible region on paper, scan and save it in your computer.

Copy the image (Graph) and paste it onto the worksheet named P5-Graph

(b) Write all the vertices of the feasible region and identify the optimal vertex

What is the optimal objective function value?

Vertex

x1

x2

x1

x2

1

optimal vertex

2

3

optimal objective fuction value

P4-Graph

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