62at (x₁, x₂)6(b) Find the optimal solution to the LP Relaxation. (Round your answers to three decimal places.)at (x₁, x₂) ==8Using this solution, round down to find a feasible integer solution.(c) Find the optimal integer solution.at (x₁, x₂)X₁ Consider the following all-integer linear program.5X1 + 8X2Maxs.t.86x₁ + 5x₂ < 359x1 + 4x₂ < 361x₁ + 2x₂ ≤ 12X₁, X₂0 and integer(a) Graph the constraints for this problem. Use points to indicate all feasible integer solutions.X2X₂2468X18642468X2862268X1

By graphing the constraints and the objective function, one can solve linear programming problems…

Answered: 2 6 |at (x₁, x₂) = | 8 (b) Find the…

Practical Management Science

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Chapter2: Introduction To Spreadsheet Modeling

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Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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For the remaining questions, consider the following problem description: An oil company is considering exploring new well sites S₁, S2, ..., S10 with respective costs C1, C2, C10. And in particular they want to find the least-cost selection of 5 out of the 10 possible sites. The binary decision variables x₁,x2,..., X10 denote the decision to explore the corresponding site.
a.) Formulate a LP model of this problem
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Use simplex method for linear programming. Show solution for each iteration table. Problem: A small firm that assembles computers is about to start production of two new types of personal computers. Each type will require assembly time, inspection time, and storage space. The amount of each of these resources that can be devoted to the production of the computers is limited. The manager of the firm would like to determine the quantity of each computer to produce in order to maximize the profit generated by sales of these computers. In order to develop a suitable model of the problem, the manager has met with design and manufacturing personnel. As a result of those meetings, the manager has obtained the following information: Type 1 Type 2 Profit per unit $60 $50 Assembly time per unit 4 hours 10 hours Inspection time per…
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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.
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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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2 6 |at (x₁, x₂) = | 8 (b) Find the optimal solution to the LP Relaxation. (Round your answers to three decimal places.) at (x₁, x₂) = | (c) Find the optimal integer solution. | at (x₁, x₂) = | X1 Using this solution, round down to find a feasible integer solution.