Problem 1. You are given the following linear programming problem regarding production of two products X1 and X2.Maximize Z= $46X1 + $69X2Subject to:4X1+ 6X2 ≤ 84 (Time in department 1)2X1+1 X2 2 20 (Time in Department 2)4X1≤ 60 (Time in Department 3)Using graphical procedure, solve the problem. (Graph the constraints and identify the region of feasiblesolutions). What are the values of X1, X2 the three slacks S1, S2, S3, and the value of the objective function(Z) at optimum? If there are multiple optimum solutions, please give two of the optimum solutions.YOUR ANSWERS:O Optimum solution 1:1 X1-X2=$1=S2 =5S SHOW YOUR GRAPH BELOW:S3=Z=23 Optimum solution 2: (if there is a second optimum solution)X1 =X2 =$1=S2=S3-Z-

Answered: Image /qna-images/answer/55662051-5e45-43a8-870c-a336e0873986.jpg

Answered: Maximize Z-$46X1 + $69X2 Subject to:…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter5: Network Models

Section5.5: Shortest Path Models

Problem 32P

See similar textbooks

Similar questions

Next question Use the simplex method to solve the linear programming prob z= 8x1 - 7x2 + 4x3 2x1 Maximize X2 + 8x3 s 40 4x1 - 5x2 + 6x3576 2x1 - 2x2 + 6x3< 32 X120, X2 20, хз 20. subject to Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A. The maximum is , X2 =, X3 = S2 = and s3 when X1 S1 = B. There is no maximum.
L.P. Model: Maximize Subject to: Z = 8X+6Y 1X + 2Y ≤8 5X +4Y ≤20 X,Y 20 (C₁) (C₂) On the graph on right, the constraints C, and C₂ have been plotted. Using the point drawing tool, plot the four corner points for the feasible area. The optimum solution is: X= 4 (round your response to two decimal places). Y = (round your response to two decimal places). 20- 18- 16- 14- 12+ >10- 8- 6- 0 2 4 6 8 10 X 12 14 16 18 20 2
Define Linear programming (LP)?
Four qualified postgraduate students are to be allocated to four professors. The preference given by student (scale 1-10) is shown as table below. Student A В C D Professor James Jordan Janet 7 8 6. Jessy 5 8. 7 (a) Formulate a linear programming model for the problem. [NOTE: Please use x, where i = 1, 2,...,n -Professor and j=1, 2,...,m -Student to represent your decision variables.] (b) From the output below, what is the optimal allocation plan and what is the total preference scales obtained from the allocation plan? Model Variable Original Value Final Value Value x11 1 1 Value x12 1 Value x13 1 Value x14 Value x21 Value x22 Value x23 1 1 1 1 1 Value x24 1 Value x31 Value x32 Value x33 1 1 1 1 Value x34 1 Value x41 1 Value x42 1 Value x43 1 Value x44 1 1 699 445
Problem 8-21 (Algorithmic) Round Tree Manor is a hotel that provides two types of rooms with three rental classes: Super Saver, Deluxe, and Business. The profit per night for each type of room and rental class is as follows: Rental Class Room Super Saver Deluxe Business Type I $30 $35 — Type II $20 $30 $40 Type I rooms do not have wireless Internet access and are not available for the Business rental class. Round Tree's management makes a forecast of the demand by rental class for each night in the future. A linear programming model developed to maximize profit is used to determine how many reservations to accept for each rental class. The demand forecast for a particular night is 130 rentals in the Super Saver class, 60 rentals in the Deluxe class, and 50 rentals in the Business class. Round Tree has 100 Type I rooms and 120 Type II rooms. Use linear programming to determine how many reservations to accept in each rental class and how the reservations should be…
Maximize profit = 4X + 4Y Subject to: 3X +5Y ≤ 150 X – 2Y ≤ 10 5X + 3Y ≤ 150 X, Y ≥ 0 Required: a- The corner point method to obtain the optimal point. b- Specify the profit value. c- Calculate the Slack for each constraint and state its formula.
Problem 4-15 (Algorithmic) Seastrand Oil Company produces two grades of gasoline: regular and high octane. Both gasolines are produced by blending two types of crude oil. Although both types of crude oil contain the two important ingredients required to produce both gasolines, the percentage of important ingredients in each type of crude oil differs, as does the cost per gallon. The percentage of ingredients A and B in each type of crude oil and the cost per gallon are shown. Crude Oil Cost Ingredient A Ingredient B 1 $0.15 40% 40% 2 $0.20 70% 10% Each gallon of regular gasoline must contain at least 60% of ingredient A, whereas each gallon of high octane can contain at most 30% of ingredient B. Daily demand for regular and high-octane gasoline is 900,000 and 500,000 gallons, respectively. How many gallons of each type of crude oil should be used in the two gasolines to satisfy daily demand at a minimum cost? Round your answers to the nearest whole number. Round the…
1. A manufacturing company is engaged in producing three types of products: X, Y and Z. The production department produces, each day, components sufficient to make 50 units of X, 25 units of Y and 30 units of Z. The management is confronted with the problem of optimizing the daily production of the products in the assembly department, where only 100-man-hours are available daily for assembling the products. The following additional information is available Type of Product Profit Contribution Assembly Time per Product (Hrs) per Units of Products (in PhP) 120 0.8 Y 200 1.7 450 2.5 The company has a daily order commitment for 20 units of product X and a total of 15 units of products Y and Z. Formulate this problem as an LP model so as to maximize the total profit. Using simplex method, find the number of units of product X, Y and Z to product to maximize total profit.
L.P. Model: Maximize Z= 8X+2Y Subject to: 1X+2Y≤6 (C1) 5X+1Y≤20 (C2) X,Y≥0 On the graph on right, the constraints C1 and C2 have been plotted. Using the point drawing tool, plot the four corner points for the feasible area. The optimum solution is: X = (round your response to two decimal places). Y = (round your response to two decimal places). Optimal solution value Z = (round your response to two decimal places).
Problem 3-19 (Algorithmic) Better Products, Inc., manufactures three products on two machines. In a typical week, 40 hours are available on each machine. The profit contribution and production time in hours per unit are as follows: Category Profit/unit Machine 1 time/unit Machine 2 time/unit Product 1 2 3 Two operators are required for machine 1; thus, 2 hours of labor must be scheduled for each hour of machine 1 time. Only one operator is required for machine 2. A maximum of 90 labor-hours is available for assignment to the machines during the coming week. Other production requirements are that product 1 cannot account for more than 50% of the units produced and that product 3 must account for at least 10% of the units produced. a. How many units of each product should be produced to maximize the total profit contribution? If required, round your answers the nearest whole number. If your answer is zero, enter "0". Profit = $ $ Machine 2 What is the projected weekly profit associated…
(c) Suppose that management wants to provide additional security coverage for room 7. Specifically, management wants room 7 to be covered by two cameras. Which constraint would have to change? O Room 1 O Room 2 O Room 3 O Room 4 O Room 5 O Room 6 O Room 7 O Room 8 What should the new constraint be? (d) With the policy restriction specified in part (c), determine how many two-way camera systems will need to be purchased and where they will be located. The gallery should install cameras with (X₁, X2, X3, X4, X5, X6, X7, X8, X9, X10, X11 X12, X13) =
eBook Problem 8-21 (Algorithmic) Round Tree Manor is a hotel that provides two types of rooms with three rental classes: Super Saver, Deluxe, and Business. The profit per night for each type of room and rental class is as follows: Room Type 1 Type II Rental Class Super Saver $37 $18 Explain. Deluxe $40 $33 Variable SuperSaver rentals allocated to room type I SuperSaver rentals allocated to room type II Deluxe rentals allocated to room type I Deluxe rentals allocated to room type II Business rentals allocated to room type II Is the demand by any rental class not satisfied? Business Type 1 rooms do not have wireless Internet access and are not available for the Business rental class. Round Tree's management makes a forecast of the demand by rental class for each night in the future. A linear programming model developed to maximize profit is used to determine how many reservations to accept for each rental class. The demand forecast for a particular night is 125 rentals in the Super Saver…

SEE MORE QUESTIONS

Recommended textbooks for you

Practical Management Science

Operations Management

ISBN:

9781337406659

Author:

WINSTON, Wayne L.

Publisher:

Cengage,

Practical Management Science

Operations Management

ISBN:

9781337406659

Author:

WINSTON, Wayne L.

Publisher:

Cengage,

SEE MORE TEXTBOOKS