Ingenieria En Sistemas

Ch. 2 – Practice Problems/Notes

Real – Life Application – Frontier Airlines Purchases Fuel Economically (Chapter 26/online)

Practice problems

2.1A

2. Determine the best feasible solution among the following (feasible and infeasible) solutions of the Reddy Mikks model:

a. x1 = 1, x2 = 4. (infeasible)

b. x1 = 2, x2 = 2. (feasible); z = 18

c. x1 = 3, x2 = 1.5. (feasible); z = 21, optimum solution from presented choices.

d. x1 = 2, x2 = 1. (feasible); z = 14

e. x1 = 2, x2 = -1. (infeasible)

Tora moment – pg. 18,19

2.2A

4. A company that operates 10 hours a day manufactures two products on three sequential processes. The following table summarizes the data of the problem:

Minutes per unit

Product Process 1 Process 2 Process 3 Unit profit

1 10 6 8 $2

2 5 20 10 $3

Determine the optimal mix of the two products.

Maximize Optimum solution Z = 2x1 + 3x2

Subject to

10x1 + 5x2 ≤ 600

6x1 + 20x2 ≤ 600

8x1 + 10x2 ≤ 600

x1, x2 ≥ 0

Optimum mix is at point 2.

6. Alumco manufactures aluminum sheets and aluminum bars. The maximum production capacity is estimated at either 800 sheets or 600 bars per day. The maximum daily demand is 550 sheets and 580 bars. The profit per ton is $40 per sheet and $35 per bar. Determine the optimal daily production mix.

Maximize Optimum solution Z = 40x1 + 35x2

Subject to

600 ≤ 0.75x1 + x2 ≤ 800

x1 ≤ 550

x2 ≤ 580

x1, x2 ≥ 0

(Using the graphical method as presented by prior question; and neglecting (550,0), & (0,580))

1. x1 = 26.67, x2 = 580; Z = $21,366.80

2. x1 =550, x2 = 187.5; Z = $28,562.50  Optimum mix

2.2B

4. John must work at least 20 hours a week to supplement his income while attending school. He has the opportunity to work in two retail stores. In store 1, he can work between 5 and 12 hours a week, and in store 2, he is allowed between 6 and 10 hours. Both stores pay the same hourly wage. In deciding how many hours to work in each store, John wants to base his decision on work stress. Based on interviews with present employees, John estimates that, on an ascending scale of 1 to 10 , the stress factors are 8 and 6 at stores 1 and 2, respectively. Because stress mounts by the hour, he assumes that the total stress for each store at the end of the week is proportional to the number of hours he works in the store. How many hours should John work in each store?

Minimize Optimum solution Z = 8x1 + 6x2

Subject to

5 ≤ x1 ≤ 12

6 ≤ x2 ≤ 10

x1 + x2 ≤ 20

x1, x2 ≥ 0

(Using the graphical method as presented by 2.2A #4, however searching for minimization

...