Recall the following problem from Homework 2: Consider a window company with onl
ID: 473371 • Letter: R
Question
Recall the following problem from Homework 2: Consider a window company with only three
employees which makes two dierent kinds of hand-crafted windows: a wood-framed and an aluminum-
framed window. They earn $60 prot for each wood-framed window and $30 prot for each aluminum-framed
window. Employee 1 makes the wood frames, and can make 6 per day. Employee 2 makes the aluminum
frames, and can make 4 per day. Employee 3 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.
Let x1 and x2 be the number of wood-framed and aluminum-framed windows, respectively. The linear
programming model can be formulated as:
maximize 60x1 + 30x2
subject to 6x1 + 8x2 <=48
x1 <=6
x2 <= 4
x1; x2 >= 0
The optimal solution to this problem is (x1; x2 ) = (6; 1: 5), with an optimal cost of 405.
a) Suppose that one day, Employee 1 oers to work overtime to produce up to 9 wood frames instead of 6,
but asks that he be paid an extra xed amount of $90. Can his oer be evaluated without re-solving the
model? Explain why or why not.
b) Suppose that on a dierent day, Employee 1 oers to work overtime to produce up to 7 wood frames
instead of 6, but asks that he be paid an extra xed amount of $30. Is this a good deal from the company's
point of view?
c) What would be the change in total prot if the company agreed to Employee 1's oer from part b)?
Explanation / Answer
Answer:
By given optimum solution,
Sale Price each Unit of X1 & X2
Total Cost for 7.5 Units = $405/7.5 Units = $ 54 Each unit for X1
= $54/2 = $ 27 for X2
a) offer of employee 1 cannot be evaluated without re-solving the model as limiting factors have changed by offer of production of 9 Units with extra payment of $90.
b) Yes, it is good deal from company's point of view as profit on product X1 is $60 and demand by Emloyee 1 is $ 30 only provided Employee 3 is ready to produce extra 6 squire feet of Glass for less than $30 for this 1 unit of X1 as he has already reached his limit of 48 Squire feet of Glass (6x 6 for X1 + 8x 1.5 for X2).
c) Total Profit of the company will increase by $30 if Employee 3 is ready to produce extra 6 squire feet of glass without any charges.
Product No. of Unit Profit Cost Price Per Uint Sale Price Per Unit X1 6 $60.00 $54.00 $114.00 X2 1.5 $30.00 $27.00 $57.00Related Questions
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