Assignment – 1 ( Answer the following questions )
Decision Science (BSG 305)
Assignment 1 (8 Marks) CLO3 CLO4
Instructions
I. Clearly state the answers to the assignment questions and submit your work in a hardcopy
II. Due date: Due on Wednesday 11 April 2016 ( I will not accept any work after the deadline)
III. Answer all questions
IV. Don’t forget to write your name, your ID and the assignment number in your answer sheet.
Q1. The Whitt Window Company is a company with only three employees which makes two different kinds of hand-crafted windows:
a wood-framed and an aluminum-framed window. They earn $60 profit for each wood-framed window and $30 profit for each Aluminum-framed window.
– Doug makes the wood frames, and can make 6 per day.
– Linda makes the aluminum frames, and can make 4 per day.
– Bob forms and cuts the glass, and can make 48 square feet of glass per day.
Each wood-framed window uses 6 square feet of glass and each aluminum-framed window uses 8 square feet of glass.

(a) Identifying both the activities and the resources (construct and fill in a table)
(b) Is this problem can be solved using a linear programming model and why. If yes
Formulate the linear programming model.

Q2. A small company produces only two sizes of frames for stereo receivers: standard size and slim-line. The accounting department has provided the following table for the price and unit cost of the products:

Standard Slim-line
Selling Price $6.00 $4.25
Raw Materials $0.75 $0.50
Packaging $0.25 $0.25

Since the company is paying each employee $1200 per month, independent of their productivity, labor cost is excluded from profit margin calculations. The company has 350 units of raw material and 8 hours of labor available each day for production. In order to produce a standard frame 0.4 labor-hr and 1.5 units of raw material are required. Similarly for one slim-line frame production 0.25 labor-hours and 1 unit of raw material are required. Formulate a linear programming model to solve this problem.

Q3. Ahmed wants to buy x oranges and y peaches from the store. He must buy at least 5 oranges and the number of oranges must be less than twice the number of peaches. An orange weighs 150 grams and a peach weighs 100 grams. Ahmed can carry not more than 3.6 kg of fruits home. Write the linear program model constrains for this problem?
Q4. A calculator company produces a scientific calculator and a graphing calculator. Long-term projections indicate an expected demand of at least 100 scientific and 80 graphing calculators each day. Because of limitations on production capacity, no more than 200 scientific and 170 graphing calculators can be made daily. To satisfy a shipping contract, a total of at least 200 calculators much be shipped each day. If each scientific calculator sold results in a $2 loss, but each graphing calculator produces a $5 profit, how many of each type should be made daily to maximize net profits?

Q5. Consider the following transportation table computes the least cost using MODI method
A B C Supply
1 $1 $3 $4 13
2 $4 $1 $3 17
Demand 10 10 10 Total 30