LAGUADOR, EDJAY A.
BSA 3RD YEAR
Assignment:
Bataan Sporting Equipment Inc., makes two different types of baseball gloves. A regular
model and special model. The firm has 54,000 minutes of production time available in its cutting
and sewing department, 18,000 minutes available in its finishing department, and 6,000 minutes
available in its packaging and shipping department. The production time requirement and the
profit contribution per glove are given in the table below.
Assuming that the company is interested in maximizing the total profit contribution, answer the
following questions:
1. What is the linear programming model for this problem?
2. How many gloves of each model should the Bataan Company manufacture?
3. What is the total profit contribution Bataan Company earn with the given production
quantities?
4. How many minutes of production time will be scheduled in each department?
5. What is the slack time in each department?
Answer:
1. Question: What is the linear programming model for this problem?
Maximize: Z= 50x + 80y 1st Constraint
Subject to: 68x + 90y < 54,000 (Cutting and Sewing Department)
30x + 20y < 18,000 2nd Constraint
7.5x + 15y < 6,000 (Finishing Department)
x, y > 0 3rd Constraint
(Packaging and Shipping Department)
Constraint 1
30x + 20y = 18,000
68x + 90y = 54,000 30x + 20(0) = 18,000
68(0) + 90y = 54,000 X= 600
Y = 600 X intercept = (600, 0)
Y intercept = (0,600)
Constraint 3
68x + 90y = 54,000
68x + 90(0) = 54,000 7.5x + 15y = 6,000
X = 794 7.5(0) + 15y = 6,000
X intercept = (794, 0) Y = 400
Y intercept = (0,400)
Constraint 2
7.5x + 15y = 6,000
30x + 20y = 18,000 7.5x + 15(0) = 6,000
30(0) + 20y = 18,000 X = 800
Y= 900 X intercept = (800, 0)
Y intercept = (0,900)
*I choose the variable that can be easily eliminated. I Eliminate x by multiplying equation 3 by (-4) bring
down equation 2 then add. Substitute 150 in place of y in any of the two equations to get the coordinate
point of c (500,150).
30x + 20y = 18,000
7.5x + 15y = 6,000
7.5x + 15y = 6,000
7.5(-4) + 15 (-4) = 6,000 (-4)
-30x – 60y = -24,000
30x + 20y = 18,000
-40y = -6,000
Y = 150
30x + 20y = 18,000
30x + 20 (150) = 18,000
30x + 3,000 = 18,000
30x = 18,000-3,000
X = 500
Test Area ABCD
Z = 50x + 80y
Point A (0, 0) 50(0) + 80 (0) = 0
Point B (0, 400) 50(0) + 80 (400) = 32,000
Point C (500, 150) 50(500) + 80 (150) = 37,000
Point D (600, 0) 50(600) + 80 (0) = 30,000
2. Question: How many gloves of each model should the Bataan Company manufacture?
The company will produce:
X = 500 regular model of baseball gloves and
Y = 150 special model of baseball gloves
3. Question: What is the total profit contribution Bataan Company earn with the given
production quantities?
The company will earn 37,000.
Solution:
Where x= 500 and y=150
Substitute:
50(500) + 80(150)
25,000 + 12,000
= 37,000
4. Question: How many minutes of production time will be scheduled in each department?
Schedule time per production:
Constraint 1 (Cutting and Sewing Department)
68x + 90y
68(500) + 90(150)
34,000 + 13,500
= 47,500 minutes
Constraint 2 (Finishing Department)
30x + 20y
30(500) + 20(150)
15,000 + 3,000
= 18,000 minutes
Constraint 3 (Packaging and Shipping Department)
7.5x + 15y
7.5(500) + 15(150)
3,750 + 2,250
= 6,000 minutes
5. Question: What is the slack time in each department?
Department Time Available Usage Slack Time
Cutting and Sewing 54,000 minutes 47,500 minutes 6,500 minutes
Finishing 18,000 minutes 18,000 minutes 0
Packaging and 6,000 minutes 6,000 minutes 0
Shipping
