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7–12For each of the linear programming problems in Exercises 1–6,
Maximize
(a) Set up the initial simplex tableau.
(b) Determine the particular solution corresponding to the initial tableau.
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Chapter 4 Solutions
Pearson eText for Finite Mathematics & Its Applications -- Instant Access (Pearson+)
- 23. Consider a simple economy with just two industries: farming and manufacturing. Farming consumes 1/2 of the food and 1/3 of the manufactured goods. Manufacturing consumes 1/2 of the food and 2/3 of the manufactured goods. Assuming the economy is closed and in equilibrium, find the relative outputs of the farming and manufacturing industries.arrow_forwardConsider the following mixed-integer linear program: Max 3x1 + 4x2 s.t. 4x1 + 9x2 s 36 7x1 + 4x2 s 28 x1, x2 20 and x1 integer a. Choose the correct graph which shows the constraints for this problem and uses boldface vertical lines to indicate all feasible mixed-integer solutions. (i) (ii) 7. 9. 4 5 (ii) (iv) 6 7 8 9 T0 b. Find the optimal solution to the LP Relaxation. If required, round your answers to two decimal places. The optimal solution is given by x1 = ,x2 = Its value is Round the value of x1 down to find a feasible mixed-integer solution. If required, round your answers to two decimal places. Rounding the value of x1 down to find a feasible mixed integer solution yields x1 = x2 = with a value of Is this solution optimal? Why or why not? The input in the box below will not be graded, but may be reviewed and considered by your instructor. c. Find the optimal solution for the mixed-integer linear program. If required, round your answers to two decimal places. Solution details…arrow_forwardFormulate an equivalent linear program for the following model: max min{2x3 – 1,4 – |¤1 – x2|l} – max{5x2, 3x3 – |¤1 – x2|} s.t. 5x1 + 2x2 0.arrow_forward
- Solve the following linear programming graphically [8]Minimize and maximize: z = 3x + 9ySubject to the constraints:x + 3y ≥ 6x + y ≤ 10x ≤ yx ≥ 0; y ≥ 0arrow_forwardQUESTION 14 Calculate the maximum value of 4x + 6y subject to the constraints below: 3x + y ≤ 16 x + 3y ≤ 16 y≥ 1 x ≥ 0arrow_forward[3.7] Consider the following linear programming problem: Maximize 2x₁ + x2 subject to 2x₁ + x2 XI + 4x2 XI, X2, x3 + 4x3 ≤ 6 X3 ≤ 4 X3 ≥ 0. -arrow_forward
- QUESTION 14 Calculate the maximum value of 9x + 6y subject to the constraints below: 2x + 2y s 18 x + 3y s 20 y21 x20arrow_forward.4.3 Maximize 72 + x2 +xy-8y, subject to the constraint 8-x-2y 0. The maximum value of 72+x2 + xy-8y subject to the constraint 8-x-2y 0 is. (Type an exact answer in simplified form.) Enter your answer in the answer box and then click Check Answer. All parts showing Clear Allarrow_forward1. . Solve the following linear programming model graphically: minimize Z = 3x, + 6x2 pubject to 3x, + 2x2 s 18 X + x2 2 5 X S 4 x2/x, s 7/8 X1, X2 0arrow_forward
- Solve the following linear program graphically:Minimize C = - 2X1 + 3X2Subject to X1 + X2 > 5 ---------- (1) (restriction A)X1 < 8 ---------- (2) (resource B)X2 < 3 ---------- (3) (resource C)3X1 + 9X2 < 27 ---------- (4) (resource D)Where X1, X2 > 0 5. Christy Crafty Boat Supplies has 250 yards of canvas to make sails and deck covers.There are 205 hours of labor available. The following data apply:Profit Canvas LaborSail $50 35 yards 10 hoursDeck Cover $65 10 yards 15 hoursHow many of each should be made to maximize profit?arrow_forwardSolve the linear programming problem in the attached image (excel solver or simplex tableau). Here x3 is unrestricted, so we have to take: x3=(x’3-x”3), also introduce slack and artificial variables.arrow_forwardConsider the following integer nonlinear programming problem. Маximize Z = xx3x3, XX2X3 , subject to X1 + 2x2 + 3x3< 10 x121, x 2 1, xz 2 1, and X1, X2, X3 are integers. Use dynamic programming to solve this problem. Please show your steps (show your tables).arrow_forward
- Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
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