En. Abraham Joseph Michael
Pn. Wan Noor Adzmin
TASK 1
A) Cheras Furniture Sdn. Bhd, a leader in the furniture industry, has a production plant in Setapak, Kuala Lumpur. At the particular plant, they produce two types of furniture, the dining table and the coffee table. The company is split into specific departments, each of which faces certain restrictions on manufacturing.
As a finance manager of the company, you are asked to prepare a plan of action and method of implementation in order to obtain optimum value based on the information given to you.
Labor Department : There are 75 workers in this department ( each of which works an 8 hour day ). Each dining table requires 5 hours to be produced and each coffee table requires 2 hours to be produced.
Sales : Due to supply and demand issues, the number of dining table cannot exceed three times the number of coffee tables.
Public Relation (PR) : Due to a special promotion by distributors, the number of coffee table produced each day must be at least 10.
If Cheras Furniture makes a profit of RM500 per dining table and RM200 per coffee table, how many of each should be produced, and what is the profit associated with that production?
B) Beautiful Hair Sdn. Bhd. Produces two styles of hair dryers, the Petite and the Deluxe. However, the company is facing competition from other Hair Dresses company. As a project manager you are asked to prepare a plan of action and the method of implementation in order to obtain optimum value based on the information.
The company requires 1 hour of labor to make the Petite and 2 hours of labor to make the Deluxe. The materials cost RM4.00 for each Petite and RM3.00 for each Deluxe. The profit is RM5.00 for the Petite and RM6.00 for the Deluxe. The company has 3950 labor-hours available each week and a materials budget of RM9575 per week.
How many each dryer should be made each week to maximize profit.
The Process :
Find the maximum profit ( x and y ) using inequalities and linear programming.
Use information gathered to construct a table and to write the system of inequalities.
Graph the functions and view a graphical representation of the inequality system.
Mark the feasible region and shade it.
Record the coordinates of the intersecting points.
Evaluate the objective functions at each vertex.
Record the vertex coordinates and objective function values in a table.
Find the minimum cost required or the maximum profit by comparing the objective function values.
TASK 2
A) Prepare a flowchart showing all the steps involve in solving LP using the simplex method.
B) The Cheras Furnitures Sdn. Bhd. Produces chairs and tables. Each table takes four hours of labour from the carpentry department and two hours of labour from the finishing department. Each chair requires 3 hours of carpentry and 1 hour of finishing. During the current week, 240 hours of carpentry time are available and 100 hours of finishing time. Each table produced gives a profit of RM70.00 and each chair a profit of RM50.00. How many chairs and tables should be made?
The Process :
Construct a table to summarise the information given above.
Solve the problem using the simplex method and explain each steps used to solve this problem ( recommendation and justification )
TASK 3
Balancing Nutrients
In preparing a recipe you must decide what ingredients and how much of each ingredient you will use. In these health-conscious days, you may also want to consider the amount of certain nutrients in your recipe. You may even be interested in minimizing some quantities ( like calories or fat ) or maxi-mizing others ( like carbohydrates or protein ). Linear programming techniques can help to do this. For example, consider making a very simple trail mix from dry-roasted, unsalted peanuts and seedless raisins. Table 1 lists the amounts of various dietary quantities for these ingredients. The amounts are given per serving of the ingredient.
Nutrient Peanuts Serving Size = 1 cup Rains Serving Size = 1 cup
Calories (Kcal) 850 440
Protein (g) 34.57 4.67
Fat (g) 72.50 0.67
Carbohydrates (g) 31.40 114.74
Suppose that you want to make at most 6 cups of trail mix for a day hike. You don`t want either ingredient to dominate the mixture, so you want the amount of raisins to be at least 1/2 of the amount of peanuts and the amount of peanuts to be at least 1/2 of the amount of raisins. You want the entire amount of trail mix you make to have fewer than 4000 calories, and you want to maximize the amount of carbohyddrates in the mix.
1) Let x be the number of cups of peanuts you will use, let y be the number of cups of raisins you will use, and let c be the amount of carbohydrates in the mix. Find the objective function.
2) What constraints must be placed on the objective function?
3) Graph the set of feasible points for this problem.
4) Find the number of cups of peanuts and raisins that maximize the amount of carbohydrates in the mix.
5) How many grams of carbohydrates are in a cup of the final mix? How many calories?
6) Under all these constraints given above, what recipe for trail mix will maximize the amount of protein in the mix? How many grams of protein are in a cup of this mix? How many calories?
7) Suppose you decide to eat at least 3 cups of the trail mix. Keeping the constraints given above, what recipe for trail mix will minimize the amount of fat in the mix?
8) How many grams of carbohydrates are in this mix?
9) How many grams of protein are in this mix?
10) Which of the three trail mixes would you use? Why?
