The LP model and output below represent a problem whose solution will tell a specialty retailer how many of four different styles of umbrellas to stock in order to maximize profit. It is assumed that every one stocked will be sold. The variables measure the number of women's (X1), golf (X2), men's (X3), and folding umbrellas (X4), respectively. The constraints measure storage space in units (Constraint 1), special display racks (Constraint 2), demand (Constraint 3), and a marketing restriction (Constraint 4), respectively. There is nothing you need to solve for this problem. All questions below can be answered by the output. MAX 5 X1 + 7 X2 + 6 X3 + 4.5 X4 SUBJECT TO 1) 2 X1 + 3 X2 + 3 X3 + X4 <= 120 2) 1.5 X1 + 2 X2 <= 54 3) 2 X2 + X3 + X4 <= 72 4) X2 + X3 >= 12

The LP model and output below represent a problem whose solution will tell a specialty retailer how many of four different styles of umbrellas to stock in order to maximize profit. It is assumed that every one stocked will be sold. The variables measure the number of women's (X1), golf (X2), men's (X3), and folding umbrellas (X4), respectively. The constraints measure storage space in units (Constraint 1), special display racks (Constraint 2), demand (Constraint 3), and a marketing restriction (Constraint 4), respectively. There is nothing you need to solve for this problem. All questions below can be answered by the output. MAX 5 X1 + 7 X2 + 6 X3 + 4.5 X4 SUBJECT TO 1) 2 X1 + 3 X2 + 3 X3 + X4 <= 120 2) 1.5 X1 + 2 X2 <= 54 3) 2 X2 + X3 + X4 <= 72 4) X2 + X3 >= 12

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter3: Introduction To Optimization Modeling

Section3.8: A Multiperiod Production Model

Problem 21P

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The LP model and output below represent a problem whose solution will tell a specialty retailer how many of four different styles of umbrellas to stock in order to maximize profit. It is assumed that every one stocked will be sold. The variables measure the number of women's (X1), golf (X2), men's (X3), and folding umbrellas (X4), respectively. The constraints measure storage space in units (Constraint 1), special display racks (Constraint 2), demand (Constraint 3), and a marketing restriction (Constraint 4), respectively. There is nothing you need to solve for this problem. All questions below can be answered by the output.MAX 5 X1 + 7 X2 + 6 X3 + 4.5 X4SUBJECT TO 1) 2 X1 + 3 X2 + 3 X3 + X4 <= 120 2) 1.5 X1 + 2 X2 <= 54 3) 2 X2 + X3 + X4 <= 72 4) X2 + X3 >= 12 By how much can the amount of space increase before there is a change in the dual price? You are offered an advertisement that should increase the demand constraint from 72…
The LP model and output below represent a problem whose solution will tell a specialty retailer how many of four different styles of umbrellas to stock in order to maximize profit. It is assumed that every one stocked will be sold. The variables measure the number of women's (X1), golf (X2), men's (X3), and folding umbrellas (X4), respectively. The constraints measure storage space in units (Constraint 1), special display racks (Constraint 2), demand (Constraint 3), and a marketing restriction (Constraint 4), respectively. There is nothing you need to solve for this problem. All questions below can be answered by the output. MAX 5 X1 + 7 X2 + 6 X3 + 4.5 X4 SUBJECT TO 1) 2 X1 + 3 X2 + 3 X3 + X4 <= 120 2) 1.5 X1 + 2 X2 <= 54 3) 2 X2 + X3 + X4 <= 72 4) X2 + X3 >= 12 How many men's umbrellas (X3) should be stocked? How many folding umbrellas (X4) should be stocked?
The LP model and output below represent a problem whose solution will tell a specialty retailer how many of four different styles of umbrellas to stock in order to maximize profit. It is assumed that every one stocked will be sold. The variables measure the number of women's (X1), golf (X2), men's (X3), and folding umbrellas (X4), respectively. The constraints measure storage space in units (Constraint 1), special display racks (Constraint 2), demand (Constraint 3), and a marketing restriction (Constraint 4), respectively. There is nothing you need to solve for this problem. All questions below can be answered by the output.MAX 5 X1 + 7 X2 + 6 X3 + 4.5 X4SUBJECT TO 1) 2 X1 + 3 X2 + 3 X3 + X4 <= 120 2) 1.5 X1 + 2 X2 <= 54 3) 2 X2 + X3 + X4 <= 72 4) X2 + X3 >= 12 By how much is the marketing restriction exceeded? What is the total profit?
The LP model and output below represent a problem whose solution will tell a specialty retailer how many of four different styles of umbrellas to stock in order to maximize profit. It is assumed that every one stocked will be sold. The variables measure the number of women's (X1), golf (X2), men's (X3), and folding umbrellas (X4), respectively. The constraints measure storage space in units (Constraint 1), special display racks (Constraint 2), demand (Constraint 3), and a marketing restriction (Constraint 4), respectively. There is nothing you need to solve for this problem. All questions below can be answered by the output. MAX 5 X1 + 7 X2 + 6 X3 + 4.5 X4 SUBJECT TO 1) 2 X1 + 3 X2 + 3 X3 + X4 <= 120 2) 1.5 X1 + 2 X2 <= 54 3) 2 X2 + X3 + X4 <= 72 4) X2 + X3 >= 12How many women's umbrellas (X1) should be stocked?How many golf umbrellas (X2) should be stocked?
The LP model and output below represent a problem whose solution will tell a specialty retailer how many of four different styles of umbrellas to stock in order to maximize profit. It is assumed that every one stocked will be sold. The variables measure the number of women's (X1), golf (X2), men's (X3), and folding umbrellas (X4), respectively. The constraints measure storage space in units (Constraint 1), special display racks (Constraint 2), demand (Constraint 3), and a marketing restriction (Constraint 4), respectively. There is nothing you need to solve for this problem. All questions below can be answered by the output.MAX 5 X1 + 7 X2 + 6 X3 + 4.5 X4SUBJECT TO The LP model and output below represent a problem whose solution will tell a specialty retailer how many of four different styles of umbrellas to stock in order to maximize profit. It is assumed that every one stocked will be sold. The variables measure the number of women's (X1), golf (X2), men's (X3), and folding…
The LP model and output below represent a problem whose solution will tell a specialty retailer how many of four different styles of umbrellas to stock in order to maximize profit. It is assumed that every one stocked will be sold. The variables measure the number of women's (X1), golf (X2), men's (X3), and folding umbrellas (X4), respectively. The constraints measure storage space in units (Constraint 1), special display racks (Constraint 2), demand (Constraint 3), and a marketing restriction (Constraint 4), respectively. There is nothing you need to solve for this problem. All questions below can be answered by the output.MAX 5 X1 + 7 X2 + 6 X3 + 4.5 X4SUBJECT TO 1) 2 X1 + 3 X2 + 3 X3 + X4 <= 120 2) 1.5 X1 + 2 X2 <= 54 3) 2 X2 + X3 + X4 <= 72 4) X2 + X3 >= 12 By how much can the profit on women's umbrellas increase before the solution would change? To what value can the profit on golf umbrellas increase before there is a change…
Irwin Textile Mills produces two types of cotton cloth – denim and corduroy. Corduroy is a heavier grade of cotton cloth and, as such as, requires 8 pounds of raw cotton per yard, whereas denim requires 5.5 pounds of raw cotton per yard. A yard of corduroy requires 3.6 hours of processing time; a yard of denim requires 8 hours. Although the demand for denim is practically unlimited, the maximum demand for corduroy is 600 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 $3.0 per yard of denim and $4.0 per yard of corduroy. The manufacturer wants to know how many yards of each type of cloth to produce to maximize profit. How much extra cotton, processing time, and the demand for corduroy are left over at the optimal solution after formulating a linear programming model? What is the effect on the optimal solution if the profit per yard of denim is increased from$3.0 to $4.0?
Irwin Textile Mills produces two types of cotton cloth – denim and corduroy. Corduroy is a heavier grade of cotton cloth and, as such as, requires 8 pounds of raw cotton per yard, whereas denim requires 5.5 pounds of raw cotton per yard. A yard of corduroy requires 3.6 hours of processing time; a yard of denim requires 8 hours. Although the demand for denim is practically unlimited, the maximum demand for corduroy is 600 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 $3.0 per yard of denim and $4.0 per yard of corduroy. The manufacturer wants to know how many yards of each type of cloth to produce to maximize profit. Formulate a linear programming model for this problem. Solve the problem by using the
Irwin Textile Mills produces two types of cotton cloth – denim and corduroy. Corduroy is a heavier grade of cotton cloth and, as such as, requires 8 pounds of raw cotton per yard, whereas denim requires 5.5 pounds of raw cotton per yard. A yard of corduroy requires 3.6 hours of processing time; a yard of denim requires 8 hours. Although the demand for denim is practically unlimited, the maximum demand for corduroy is 600 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 $3.0 per yard of denim and $4.0 per yard of corduroy. The manufacturer wants to know how many yards of each type of cloth to produce to maximize profit. Formulate a linear programming model for this problem. Solve the problem by using excel / the computer
CWD agro. produces two pepper sauces, Hot Scorpion and Mad Devil. These sauces are both made by blending two ingredients, A and B. A certain level of flexibility is permitted in the formulae for these products. The allowable percentages, along with revenue and cost data, are given in the following table. Up to 80 quarts of A and 60 quarts of B could be purchased. Saddam can sell as much of these sauces as it produces. Formulate an LP whose objective is to maximize the net profit from the saleof the sauces. Sauce Ingredient A Ingredient B Sales Price Per Quart (s) Hot Scorpion At least 35% At least 50% 7.00 Mad Devil At most 70% At least 40% 5.70 Cost per quart $3.20 $5
Irwin Textile Mills produces two types of cotton cloth—denim and corduroy. Corduroy is a heavier grade of cotton cloth and, as such, requires 7.5 pounds of raw cotton per yard, whereas denim requires 5 pounds of raw cotton per yard. A yard of corduroy requires 3.2 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 5,500 pounds of cotton and 3,000 hours of processing time available each month. The manufacturer makes a profit of $2.25 per yard of denim and $3.10 per yard of corduroy. The manufacturer wants to know how many yards of each type of cloth to produce to maximize profit. Due to the market change, the demand for corduroy has increased to 600 yards per month. How would this affect Irwin Textile Mills' profits? Question 2 options: Cannot decide. Profits would decrease. Profits…
Irwin Textile Mills produces two types of cotton cloth—denim and corduroy. Corduroy is a heavier grade of cotton cloth and, as such, requires 7.5 pounds of raw cotton per yard, whereas denim requires 5 pounds of raw cotton per yard. A yard of corduroy requires 3.2 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 5,500 pounds of cotton and 3,000 hours of processing time available each month. The manufacturer makes a profit of $2.25 per yard of denim and $3.10 per yard of corduroy. The manufacturer wants to know how many yards of each type of cloth to produce to maximize profit. If Irwin Mills could obtain only 5,000 pounds of cotton per month, at the optimal solution, the value of X2 is: (refer to slides #17-19 for the clue) Question 3 options: 456 510 1,000 0