Formulate and solve the model for the following problem: Irwin Textile Mills pro
ID: 3142361 • Letter: F
Question
Formulate and solve the model for the following problem: Irwin Textile Mills produces two types of cotton cloth denim and corduroy. Corduroy is a heavier grade of cotton cloth and, as such, requires 8 pounds of raw cotton per yard, whereas denim requires 6 pounds of raw cotton per yard. A yard of corduroy requires 4 hours of processing time; a yard of denim requires 3.0 hours. Although the demand for denim is practically unlimited, the maximum demand for corduroy is 510 yards per month. The manufacturer has 6,500 pounds of cotton and 3,000 hours of processing time available each month. The manufacturer makes a profit of $2.5 per yards of denim and $3.25 per yard of corduroy. The manufacturer wants to know how many yards of each type of cloth to produce to maximize profit. Formulate the model and put it into standard form. Solve it a. How much extra cotton and processing time are left over at the optimal solution? Is the demand for corduroy met? b. If Irwin Mills can obtain additional cotton or processing time, but not both, which should it select? How much? Explain your answer. C. If Irwin Mills can obtain additional cotton or processing time, but not both, which should it select? How much? Processing Time or additional cotton? How much?
Explanation / Answer
X = # of yards of denim
Y = # of yards of Corduroy
Max. Profit: Z = 2.25 * X + 3.25 * Y, subject to Max. Demand for Corduroy: 0 <= Y <= 510 and x >= 0
Raw Cotton in lbs: 6x + 8Y <= 6500
Processing Time in hours: 3X + 4Y <= 3000 or 6x + 8Y <= 6000
for Y=510 , x = (6000-8*510)/6 = 320
Maximum Profit = 2.25*320+ 3.25*510 =2377.5 dollars
Amount of cotton left = 6500 - ( 6*320 +8*510)= 500 lbs and No processign time left
The demand for Curduroy is met
If Irwin Mills can obtain additional cotton or processing time, but not both, it should select extra time because cotton is already left
additional processing time should be equal to time left for making denims from remaing cotton because demand of curduroy is already met
cotton left = 500, denim that can be made out of it = 500/8 = 62.5 yrds
time needed to make that much denim = 62.5*4 = 250 hours