2(b) Solve the LP Relaxation of this problem.] at (x₂₁x₂)-([(c) Find the optimal integer solution.] at (x₁₂₁x₂)-([8 Consider the following all-integer linear program+ 1₂Max 1st.3x₂+6₂5311x, 5₂202x+14₂51120 and integer(a) Grach the constraints for this problem. Use dots to indicate all feasible integer solutionsDo20

To choose: (a) The graph of the constraints. (b) To solve the LP relaxation of the problem. (c) The…

Answered: Consider the following all integer…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter7: Nonlinear Optimization Models

Section: Chapter Questions

Problem 60P

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1. If constraint has a shadow price of $6, Right-Hand-Side (RHS) is 12, allowable increase is 2, allowable decrease is 4. How would objective function change if the RHS of this constrains changes from 12 to 9? Answer___________
Suppose we are solving a maximization problem andthe variable xr is about to leave the basis.a What is the coefficient of xr in the current row 0?b Show that after the current pivot is performed, thecoefficient of xr in row 0 cannot be less than zero.c Explain why a variable that has left the basis on agiven pivot cannot re-enter the basis on the next pivot.
In problems involving maximization and minimization, what is the objective function? States intended outcome in equation form Incorporates constraint of maximum budget Lists set of potential restrictions on the solution Cites constraints to ensure objectivity
2(a) The tableau is not optimal for either maximization or a minimization problem. Thus, when a non-basic variable enters the solution it can either increase or decrease Z or leave it unchanged, depending on the parameters of the entering non basic variable. Basic x1 X2 X3 X4 X5 X6 X7 X8 solution -5 4 -1 -10 620 X8 3 -2 -3 -1 1 12 X3 1 1 3 1 3 X1 1 -1 -4 (i)Categorize the variables as basic and non-basic and provide the current values of all the variables. (ii)Assuming that the problem is of the maximization type, identify the non- basic variables that have the potential to improve the value of Z. If each such 3 variable enters the basic solution, determine the associated leaving variable, if any, and the associated change in Z. (iii)Repeat part (b) assuming that the problem is of the minimization type. (iv)Which non basic variable(s) will not cause a change in the value of Z when selected to enter the solution? (b) Let xij be the amount shipped from source i to destination j in a 5X5…
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Formulate a linear program for this problem. 2) A hydroelectric dam needs to schedule how much power to produce in each of the next 24 hours. The demand in megawatts (MW) in hour t = 1, ..., 24 is dị. The power plant must produce at least the demand for each hour, but can produce more at a cost of K dollars per excess MW. For engineering reasons (can't open/close waterways too fast), after hour 1 the production in any given hour must be within 10 MW of the previous hour's production. For example, producing 25 MW in hour 3 means in hour 4 we have to produce between 15 and 35 MW. Finally, the combined production over 24 hours cannot exceed the reservoir capacity R. Please note that d, K, R are parameters, i.e. known values.
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Your Manufacturing company has been tasked with building Televisions, computers, and microwaves. To make these products, there are three sub components: Capacitors, Resistors, and Processors. Below shows the maximum number of Televisions, computers, and microwaves we can make along with the maximum number of capacitors, resistors, and processors available to make them. Your Revenue function is determined as $2 for every capacitor used, $3 for every resistor, and $25 for each processor. However, there are FIXED costs if you decide to use the these. If you use Capacitors, it will have a fixed cost of $50, Resistors will have a fixed cost of $60, and Processors have a fixed cost of $250. The total profit is Revenue - Cost. Objective: Determine how many Capacitors, resisters, and processors to use in order to maximize profit. You will also need to capture if you choose to use Capacitors (SC), Resistors (SR), and Processors (SP). (NOTE: The profit is made up of 6 numbers: First three for…
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Pi Basic Variables Quantity 4 2 y S1 S2 4 4 -1 S2 1 1 Zj Pj Zj 16 4 -4 4 The pivot column in a maximization problem is the column with the greatest non-negative Pj - Zj. the greatest negative Pj - Zj. the greatest negative Zj. the greatest non-negative Zj.
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Innis Investments manages funds for a number of companies and wealthy clients. The investment strategy is tailored to each client's needs. For a new client, Innis has been authorized to invest up to $1.2 million in two investment funds: a stock fund and a money market fund. Each unit of the stock fund costs $50 and provides an annual rate of return of 10%; each unit of the money market fund costs $100 and provides an annual rate of return of 4%. The client wants to minimize risk subject to the requirement that the annual income from the investment be at least $60,000. According to Innis' risk measurement system, each unit invested in the stock fund has a risk index of 8, and each unit invested in the money market fund has a risk index of 3. The higher risk index associated with the stock fund simply indicates that it is the riskier investment. Innis's client also specified that at least $300,000 be invested in the money market fund. Refer to the computer solution shown below. Optimal…

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Consider the following all integer linear program Max 20₁ 20₂ St. S₁+0₂531 1x, 5x₂20 2, 14, 11 20 and integer (a) Graph the constraints for this problem. Use dots to indicate all feasible eger solution DO