Tony Starks company makes two types of bullet proof iron sui

Tony Stark’s company makes two types of bullet proof “iron suits”: Super Red and Invincible Blue. These iron suits are made of two types of special metals: metal A and metal B. Each Super Red suit requires 3 pounds of metal A and 1 pound of metal B. Each Invincible Blue suit requires 1 pound of metal A and 2 pounds of metal B. The profit for each Super Red suit is $100 dollars and the profit for each Invincible Blue suit is $120. Due to government regulations, Tony can only obtain 450 pounds of metal A and 300 pounds of metal B per month. Tony also needs to produce at least 50 Invincible Blue suits per month to fulfill a government contract. The demand for the iron suits is high and all the suits made will be sold. As Tony’s Chief Operations Officer, Tony wants you to find a production plan (i.e., the number of suits for each type to produce) to maximize his monthly profit.

You decide to formulate the production planning problem as a linear program, and define the decision variable as follows.

Let x be the number of Super Red suits to make per month.

Let y be the number of invincible Blue suits to make per month.

1. What is the objective function?

A) max x + y

B) max 100x + 120y

C) max 120x + 100y

D) max 300x + 450y

Next, choose answers for 7.3.b-7.3.e from the following equations

A) x + y 450

B) x + y 300

C) 3x + y 450

D) x + 2y 300

E) y 50

F) x 0

G) x 6= 0

2.Which constraint represents metal A’s availability?

3. Which constraint represents metal B’s availability?

4. Which constraint represents the minimum requirement of Invincible Blue suits?

5. Which constraint represents the non-negativity constraint for the quantity of Super Red suits?

After you answer the above questions, you would have the complete formulation (objective function and constraints) of the linear program. The following steps will help you find the optimal solution for the production plan.

• Draw the constraint lines.

• Shade the feasible region of this linear program

• Draw a line that has a same slop as the objective function [hint: draw the profit line that equal to 12000]

• Utilize the objective function line to find the optimal solution of x and y. Don’t simply eyeball the answer. You should find the exact solution by solving the two equations (constraints) for the intersection point.

6. Report the maximum profit at the optimal solution.

Solution

Sol)

Let x be the number of Super Red suits to make per month.

Let y be the number of invincible Blue suits to make per month.

1) The profit for each Super Red suit is $100 dollars and the profit for each Invincible Blue suit is $120.

Ans) The objective function is  max 100x + 120y

2) Which constraint represents metal A’s availability?

Tony can only obtain 450 pounds of metal A and Each Super Red suit requires 3 pounds of metal A and 1 pound of metal B

Ans) 3x + y 450.

3)  300 pounds of metal B per month and  Each Invincible Blue suit requires 1 pound of metal A and 2 pounds of metal B

Sol) x + 2y 300

4) constraint represents the minimum requirement of Invincible Blue suits

SOl)  y 50