LP. Model: Minimize Subject to: Z= 1X₁ + 1x₂ 6X₁ + 12x₂272 1X, 20 1X, 2-1 (C₁) (C₂) (C₂) On the graph on the right, constraints C₁, C₂ and C, have been drawn using the line drawing tool. Using the point drawing tool, plot the comer points for the feasible area. X1
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- 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 )3) Maximize Z= 2x, +x2 +3x 3 X+x2+2x3 <25 + X3 5 8 X2+ x3 S10 X1, X2, X3 2 0 Subject to IMeexample 1a 1.plot all the corner points for the feasible area. 2. Find the optimum solution to X= Y= VALUE Z=
- Briefly explain these terms:a. Basic variableb. Shadow pricec. Range of feasibilityd. Range of optimality1. Given the LP model below. Do the following: a. Formulate the new LP model. b. Set up the initial table then identify the optimum column, pivotal row, entering variable out, going variable, Zj row entries, and Cj n-Zj row entries Maximize eamings = $0.80xX₁ + $0.40X₂ + $1.20X3 - $0.10X4 subject to X₁ + 2X₂ + X3 + 5X₁150 X₂ 4X₂ + 8X₂ = 70 6X₁ + 7X₂ + 2X3 - X₂ 120 X₁, X₂, X₁, X₁Z 0example 14a 1. plot all the corner points for the feasible area. 2. Find the optimum solution to X= Y= VALUE Z=
- Determine the pivot element in the simplex tableau. (If there is more than one correct pivot element, choose the element with the smaller row number.) X1 X2 X3 S1 S2 3 4 2 1 15 1 20 -8 -3 10 1 row column N O Ovariables $E$11 47000 0 35 7.0000001 8.0000001 BO Constraints Final Shadow Constraint Allowable Allowable Cell Name Value Price R.H. Side Increase Decrease $B$16 LHS 55000 41 55000 10500 47000 $B$17 LHS 72000 35 72000 10500 47000 $B$18 LHS 80000 -8 80000 47000 10500 10500 $B$19 LHS 47000 0 57500 1E+30 The answers to the questions are found in this sensitivity report. Questions: Write your responses in the space provided 1. What is the range of optimality for the BN and BO variables? write your answers in this format: Lower limit <= Coefficient of BN <= Upper limit. Example 22 <= C of BN <= 40 2. What is the range of feasibility for the constraints located on B17 and B18? 3. If the right-hand side of the constraint located on B17 is decreased by 200, what is the effect on the value of the objective function?Maximize p = 7x + 6y + 3z subject to x + y + z ≤ 150 x + y + z ≥ 100 x ≥ 0, y ≥ 0, z ≥ 0. p= (x, y, z)=
- Problem 7-19 eBook Given the linear program Max 3A +48 s.t. Y -1A+ 1A + 2A + s.t. 28 ≤ 8 2B ≤ 12 18 ≤ 16 Α, Β 2 0 a. Write the problem in standard form. For those boxes in which you must enter subtractive or negative numbers use a minus sign. (Example: -300) Al+ A+ A+C A+ B+ B B+ B B b. Select the correct graph that shows the optimal solution for the problem. S1 S1 + + S₂ + S2 + S3 53 A, B, S1, S2, S3 A Q☆Please formulate this problem as an LP. (Just formulation).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___________