DR. AZMAWANI ABD RAHMAN (MGM3161)
ASSIGNMENT 1
Problem 1
Consider the following linear programming problem
Max
a.
b.
c.
8X + 7Y
s.t.
15X + 5Y
10X + 6Y
X+ Y
X, Y
<
<
<

75
60
8
0
Use a graph to show each constraint and the feasible region.
Identify the optimal solution point on your graph. What are the values of X and Y
at the optimal solution?
What is the optimal value of the objective function?
Problem 2
Maxwell Manufacturing makes two models of felt tip marking pens. Requirements for
each lot of pens are given below.
Plastic
Ink
Assembly
Molding
Time
Fliptop Model
3
5
Tiptop Model
4
4
Available
36
40
5
2
30
The profit for either model is $1000 per lot.
a.
b.
c.
What is the linear programming model for this problem?
Find the optimal solution.
Will there be excess capacity in any resource?
DR. AZMAWANI ABD RAHMAN (MGM3161)
Problem 3
Embassy Motorcycle (EM) manufacturers two lightweight motorcycles designed for easy
handling safety. The first one is called Lady –Sport model and the other one is called EZRider model. EZ-Rider engine requires 6 hours of manufacturing time and Lady-Sport
model requires 3 hour manuf`acturing time. Pasir Gudang Plant has 2100 hours of engine
manufacturing time available for the next production period.
Embassy Motorcycle frame supplier can supply as many EZ-rider frames as needed.
However, the Lady-Sport frame is more complex and the supplier can provide only up to
280 Lady-Sport frame. Final assembly and testing requires 2 hours for each EZ-Rider
model and 2.5 hours for each Lady-Sport model. A maximum of 1000 hours of assembly
and testing time are available for the next production period. The company projects a
profit contribution of RM2400 for each EZ-Rider produced and RM1800 for each LadySport produces.
1. Formulate a linear programming model
2. Find the optimal solution using the graphing procedure
3. Identify the binding constraints.
Problem 4
Chicky Farm Sdn. Bhd. is considering buying two different brands of chicken feed and
blending them to provide good, low cost diets for its chickens. Each feed contains, in
varying proportions, some or all of the three nutritional ingredients essential for fattening
chickens. Each kilograms of Brand 1 purchased, for example, contains 5 grams of
ingredient A, 4 grams of ingredient B, and ½ grams of ingredient C. Each kilograms of
brand 2 contains 10 grams of ingredient A, 3 grams of ingredient B, but no ingredient C.
The brand 1 feed costs the farm 2 cents per kilogram, while brand 2 feed costs 3 cents per
kilogram. Minimum monthly requirement for each chicken are; 90 kilograms for
ingredient A, 48 kilograms for ingredient B and 1.5 kilograms for ingredient C.
1. The owner of the farm would like to use LP to determine the lowest-cost diet that
meets the minimum intake requirement for each nutritional ingredient. Identify
the complete optimal solution
2. If the cost of brand 1 increase to 2.5 cents per kilogram, what would you advised
the owner?
3. If the cost of brand 1 decrease to 1.8 cents per kilogram and the cost of brand 2
increase to 3.5 cents per kilogram, what decision should the owner take?
4. Explain the dual price for ingredient B.
DR. AZMAWANI ABD RAHMAN (MGM3161)
Problem 5
Jati furniture sdn Bhd manufactures three types of chair: an economy model, a standard
model, and a deluxe model. The profits per unit are RM63, RM95, and RM135
respectively. The production requirements per unit are as follows:
Number of treated wood
Economy
Standard
Deluxe
1
1
1
Gallons of special
paint
1
2
4
Assembly time
8
12
14
For the coming production period, the company has 200 treated woods, 320 gallons of
special paint, and 2400 hours of assembly time available.
1. Construct your linear programming model
Refer to the computer solution below:
1.
2.
3.
4.
5.
6.
7.
8.
What is the optimal solution?
Which constraints are binding?
Which constraint shows extra capacity? How much?
If the profit for deluxe model were increased to RM150 per unit, would the
optimal solution change?
Identify the range of optimality for each objective function coefficient
Suppose the profit for economy model is increased by RM6 per unit, the profit for
standard model is decreased by RM2 per unit, and the profit for deluxe model is
increased by RM4 per unit, what will happen to the optimal solution?
Identify the range of feasibility for the right-hand-side values
If the number of treated wood available for production is increased by 100, will
the dual price for that constraint change? Explain.
DR. AZMAWANI ABD RAHMAN (MGM3161)