(Use this information to answer questions 1 to question 3) :VanMetals has $3500 available for the production of new products. Wall Inc. will buy all the products they can produce. After an initial screening, VanMetals reduced the production alternatives to tables and chairs. Each table can be produced with a cost of $400. Each chair can be produced for $350. VanMetals can devote up to 100 hours to these new products; each

table is expected to require 16 hours, and each chair is expected to require 8 hours. The

selling prices are $600 per table and $400 per chair. VanMetals's owner would like to

use all-integer linear programming without relaxation to determine the number of tables

and the number of chairs to produce to maximize revenue.

1). (7 points) What is the most relevant linear programming problem?

(a)

max (600 x + 400 y)

400 x + 350 y 3500

16 x + 8 y 100

x 4

y 9

x; y 0

(b)

max (400 x + 600 y)

400 x + 350 y 100

16 x + 8 y 3500

x 4

y 9

x; y 0

(c)

min (600 x + 400 y)

400 x + 350 y 3500

16 x + 8 y 100

x 4

y 9

x; y 0

(d)

min (400 x + 600 y)

400 x + 350 y 100

16 x + 8 y 3500

x 4

y 9

x; y 0

(Use the following LP problem to answer question 2

max 5A + 2B

subject to A 2B 420

2A + 3B 610

6A B 125

A;B 0

(7 points) What is the optimal solution and the value of objective function?

2)(a) The optimal solution is (49.25,170.5) and the value of the objective function is

587.25.

(b) The optimal solution is (43.75,137.5) and the value of the objective function is

493.75.

(c) The optimal solution is (56.75,165.5) and the value of the objective function is

614.75.

(d) The optimal solution is (60.5,163) and the value of the objective function is 628.5.

(Use the following LP problem to answer question 3 and 4

max 3X + 4Y

X + 2Y 8

X + 2Y 12

2X + Y 16

X; Y 0

3)(5 points) Value of objective function is

(a) 32.67

(b) 29.67

(c) 31.67

(d) 30.67

4)(7 points) Which of the statements on shadow price is true?

(a) Shadow price for the first constraint is zero, therefore the first constraint is binding.

Shadow price will remain the same for large increment of the right hand side of the

first constraint.

(b) Shadow price for the first constraint is zero, therefore the first constraint is not

binding. Shadow price will remain the same for large increment of the right hand

side of the first constraint.

(c) Shadow price for the first constraint is zero, therefore the first constraint is binding.

Shadow price will remain the same for large decrease in the right hand side of the

first constraint.

(d) Shadow price for the first constraint is zero, therefore the first constraint is not

binding. Shadow price will remain the same for large decrease in the right hand

side of the first constraint.