Consider the problem to the right.Maximizez= - 2x1 + 5x2- 4x3subject to- 5x2 + 2x3 s7(a) Restate the problem in terms of equations by introducing slack and surplusvariables.5x1 - X2 + 4x3 211X1 20, X2 20, X3 20.(b) Write the initial simplex tableau......(a) Fill in the blanks below.Maximizez= - 2x1 + 5x2- 4x3subject to- 5x2+ 2x3+ S1= 75x1- X2 +4x3S2= 11X1 20, x2 2 0, X3, S1 2 0, s2 20.(b) Complete the tableau below (the z column is omitted).X1X2X3S1S2

Slack and surplus variables are used for the purpose of solving Linear Programming Problems (LPP).…

Answered: Consider the problem to the right.…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter7: Nonlinear Optimization Models

Section: Chapter Questions

Problem 49P: If a monopolist produces q units, she can charge 400 4q dollars per unit. The variable cost is 60...

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If the number of competitors in Example 11.1 doubles, how does the optimal bid change?
If a monopolist produces q units, she can charge 400 4q dollars per unit. The variable cost is 60 per unit. a. How can the monopolist maximize her profit? b. If the monopolist must pay a sales tax of 5% of the selling price per unit, will she increase or decrease production (relative to the situation with no sales tax)? c. Continuing part b, use SolverTable to see how a change in the sales tax affects the optimal solution. Let the sales tax vary from 0% to 8% in increments of 0.5%.
Maximize C- 16A + 21B subject to 9A +15B $22 10A + 3B ≤ 29 and A≥0, B20. What is the optimal value of A? O 2.444 O 0.000 39.11 O 4.222
STAR Co. provides paper to smaller companies whose volumes are not large enough to warran paper rolls from the mill and cuts the rolls into smaller rolls of widths 12, 15, and 30 feet. The cutting patterns have been established: 1 2 Pattern 12ft. 15ft. 30ft. Trim Loss 0 4 1 10 ft. 3 0 7 ft. 8 0 0 4 ft. 2 1 2 1 ft. 5 2 3 1 1 ft. Trim loss is the leftover paper from a pattern (e.g., for pattern 4, 2(12)+1(15) + 2(30) = 99 hand for the coming week are 5,670 12-foot rolls, 1,680 15-foot rolls, and 3,350 30-foot rolls. hand will be sold on the open market at the selling price. No inventory is held. Number of: 3
The alternatives shown are to be compared on the basis of their present worth values. At an interest rate of 8% per year, the values of n that you should use in the uniform series factors to make a correct comparison by the present worth method are: Alternative(A) Alternative (B) -25,000 -10,000 10,000 First Cost M&O cost/year 3,000 Salvage value 6,000 -2,000 Life 4 O A n 4 years for A and n =4 years for B OB. None of the above O C. n = 4 years for A and n =3 years for B O D. n = 12 years for A and n = 12 years for B
Briefly explain these terms:a. Basic variableb. Shadow pricec. Range of feasibilityd. Range of optimality
Based on the following sensitivity analysis, which of the following products would be considered most sensitive to changes or errors in the objective function coefficient? A. Product_2 B. Product_1 C. Product_3 Variable Cells Cell Name Final Value Reduced Cost Objective Coefficient AllowableIncrease AllowableDecrease $B$2 Product_1 0 −2 25 13 5 $B$3 Product_2 175 0 25 8 9 $B$4 Product_3 0 −1.5 25 11 3 Constraints Cell Name Final Value Shadow Price Constraint R.H.Side AllowableIncrease AllowableDecrease $H$9 Resource_A 0 0 100 1E+30 100 $H$10 Resource_B 525 0 800 1E+30 275 $H$11 Resource_C 700 1.75 700 366.6666667 700
LPP Model Maximize P = 12x + 10y Subject to : 4x + 3y < 480 2x + 3y < 360 X, y 2 0 Which of the following points (x, y) is feasible? A) ( 120, 10) B ( 30, 100 ) c) ( 60, 90 ) D) ( 10, 120 )
An investor is looking to invest R 250,000 with the intent of getting the highest possible return. He plans to do this by holding a diverse stock portfolio with different hypothetical stocks with varying expected returns as seen in the table below. Stock Return earned Naspers 6% Sasol 15% ABSA 9. Capitec 3% To control for risk, the following constraints are put into place: a) No more than 15% of the total investment can be put into ABSA stocks. b) At most 40% must be invested in Sasol stocks and the Capitec stocks combined. c) The amount put in Naspers stocks must be no more than the amount invested into all the other remaining stocks combined. d) All the R250,000 must be invested and no shorting is allowed. Formulate a linear programming model for this problem to get the highest return (i.e., Define and outline your decision variables, objective function and constraints). How much of the budget should be invested into each investment option? (Show your workings in Microsoft Excel)
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2. Consider the transportation problem having the following parameter table (M is a big positive number) Source Demand 1 12345 2 3 5 1 2 3 343800 13 14 4 18 3 0 130940 Destination 4 5 22 29 18 21 M 3 5 26M940 16 M 11 24 34 19 23 11 4 6 Supply 0 ooooo 0 6 0 0 36 28 0 5 6 2 56743 (a) Use the northwest corner rule manually to obtain a complete initial BF solution, also find the objective value for this solution. How many basic variables are there in this solution? (b) Use Vogel's approximation method manually to select the first basic variable for an initial BF solution. (Attention, do not need to find an complete initial BF solution, just find the first BV for this initial BF solution)
Minimization Case. Min C = X1 + X2 + X3Subject toX1 – 3X2 + 4X3 = 5X1 – 2X2 <= 32X2 + X3 >=0And X1, X2, X3 >= 0

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