Consider the following product mix problem and its associated spreadsheet model.
Max 3X1 + 3X2
Subject to:
2X1 + 3X2 ≤ 10 (constraint #1)
3X1 + 2X2 ≤ 20 (constraint #2)
X1 ≥ 5 (constraint #3)
X1,
X2 ≥
0 (non-negativity)
Homework Answers
The correct option is C) =B2*B3+C2*C3
The problem is
Max 3X1 + 3X2
Subject to:
2X1 + 3X2 ≤ 10 (constraint #1)
3X1 + 2X2 ≤ 20 (constraint #2)
X1 ≥ 5 (constraint #3)
X1, X2 ≥ 0 (non-negativity
Add Answer to:
Consider the following product mix problem and its associated
spreadsheet model.
Max 3X1
+ 3X2
Subject to:...
Incorporate this model into a spreadsheet using the picture below as a guide for the Excel spreadsheet you develop: (th...
Incorporate this model into a spreadsheet using the picture
below as a guide for the Excel spreadsheet you develop: (the unit
profit cells have been filled in for you to give you a start).
Hint: There are SUMPRODUCT functions in the two “Resource Used”
cells, and another SUMPRODUCT function in the “Total Profit”
cell.
Hint: to answer questions parts c, d,
and e, substitute each X1 and X2 values in parts c, d, and e below
into the constraints on...
Must show all work 4. (10 pts) Consider the following problem. Minimize Z=3x2+2 xZ+X3, Maximize subject...
Must show all work
4. (10 pts) Consider the following problem. Minimize Z=3x2+2 xZ+X3, Maximize subject to subject to (constraint 1) x2+x2=7 (constraint 1) (constraint 2) 3x2+x2+x,210 (constraint 2) (constraint 3) X2-4 x32-8 (constraint 3) (constraint 4) x 21 and (all decision variables nonnegativel and x >0 (no nonnegativity constraint on x.i. (a) (5 pts) Convert this problem to a maximization problem with only three functional constraints, all constraints' RHS are non negative, and all decision variables need to satisfy...
2x1 + 4x2 + 7x3 c1: x1 +x2 +x3 ≤ 105 c2: 3x1 +4x2 +2x3 ≥...
2x1 + 4x2 + 7x3 c1: x1 +x2 +x3 ≤ 105 c2: 3x1 +4x2 +2x3 ≥ 310 c3: 2x1 +4x2 +4x3 ≥ 330 x1,x2,x3 ≥ 0 The problem was solved using a computer program and the following output was obtained variabel value reduced cost allowable increase decrease x1 0.0 -3.5 3.5 inf x2 55 0 5 7 x3 60 0 inf 5 constraint slack/surplus dual price 1 0 10 2 0 -2 3 95 0 Constraint right-hand side sensitivity constraint...
Consider the following Linear Problem Minimize 2x1 + 2x2 equation (1) subject to: x1 + x2...
Consider the following Linear Problem Minimize 2x1 + 2x2 equation (1) subject to: x1 + x2 >= 6 equation (2) x1 - 2x2 >= -18 equation (3) x1>= 0 equation (4) x2 >= 0 equation (5) 13. What is the feasible region for Constraint number 1, Please consider the Non-negativity constraints. 14. What is the feasible region for Constraint number 2, Please consider the Non-negativity constraints. 15. Illustrate (draw) contraint 1 and 2 in a same graph and find interception...
Given the following LP problem formulation and output data, perform the analysis below. Max. 100X1 +...
Given the following LP problem formulation and output data, perform the analysis below. Max. 100X1 + 120X2 + 150X3 + 125X4 s.t X1 + 2X2 + 2X3 + 2X4 < 108 (C1) 3X1 + 5X2 + X4 < 120 (C2) X1 + X3 < 25 (C3) X2 + X3 + X4 > 50 (C4) OPTIMAL SOLUTION: Objective Function Value = 7475.000 Variable Value Reduced Costs X1 8.000 0.500 X2 0.000 5.000 X3 17.000 0.000 X4 *A...
Consider the following linear programming model Max 2X1 + 3X2 Subject to: X1 + X2 &n
Consider the following linear programming model Max 2X1 + 3X2 Subject to: X1 + X2 X1 ≥ 2 X1, X2 ≥ 0 This linear programming model has: A. Infeasible solution B. Unique solution C. Unbounded Solution D. Alternate optimal solution E. Redundant constraints
samplex Problem1: Solve the following problem using simplex method: Max. z = 2 x1 + x2...
samplex
Problem1: Solve the following problem using simplex method: Max. z = 2 x1 + x2 – 3x3 + 5x4 S.t. X; + 7x2 + 3x3 + 7x, 46 (1) 3x1 - x2 + x3 + 2x, 38 .(2) 2xy + 3x2 - x3 + x4 S 10 (3) E. Non-neg. x > 0, x2 > 0, X3 > 0,44 20 Problem2: Solve the following problem using big M method: Max. Z = 2x1 + x2 + 3x3 s.t. *+...
Consider the following linear program Max 3xl +2x2 S.t 1x1 + 1x2 〈 10 3x1 1x2...
Consider the following linear program Max 3xl +2x2 S.t 1x1 + 1x2 〈 10 3x1 1x2 〈 24 1xl t 2x2< 16 And xl, x2> 0. a) Use Excel Solver to find the optimal solution to this problem. State the optimal values of xl, x2, and Z. b) Assume that the objective function coefficient for xl changes from 3 to 5. Does the optimal solution change? c) Assume that the objective function coefficient for x1 remains 3, but the objective...
Q4. (Sensitivity Analysis: Adding a new constraint) (3 marks) Consider the following LP max z= 6x1+x2 s.t.xi + x2 S5 2x1 + x2 s6 with the following final optimal Simplex tableau basis x1 r2 S2 rhs 0...
Q4. (Sensitivity Analysis: Adding a new constraint) (3 marks) Consider the following LP max z= 6x1+x2 s.t.xi + x2 S5 2x1 + x2 s6 with the following final optimal Simplex tableau basis x1 r2 S2 rhs 0 0 18 0.5 0.5 0.5 0.5 x1 where sı and s2 are the slack variables in the first and second constraints, respectively (a) Please find the optimal solution if we add the new constraint 3x1 + x2 S 10 into the LP (b)...
(b) Let E = {(1, C2, C3} be the standard basis for R3, B = {bų,...
(b) Let E = {(1, C2, C3} be the standard basis for R3, B = {bų, b2, b3} be a basis for a vector space U, and S: R3 → U be a linear transformation with the property that S(X1, X2, X3) (x2 + x3)b1 + (x1 + 3x2 + 3x3)b2 + (-3X1 - 5x2 - 4x3)b3. Find the matrix F for S relative to E and B. INSTRUCTIONS: 1. Use the green arrows next to the answer spaces below...
Incorporate this model into a spreadsheet using the picture
below as a guide for the Excel spreadsheet you develop: (the unit
profit cells have been filled in for you to give you a start).
Hint: There are SUMPRODUCT functions in the two “Resource Used”
cells, and another SUMPRODUCT function in the “Total Profit”
cell.
Hint: to answer questions parts c, d,
and e, substitute each X1 and X2 values in parts c, d, and e below
into the constraints on...
Must show all work
4. (10 pts) Consider the following problem. Minimize Z=3x2+2 xZ+X3, Maximize subject to subject to (constraint 1) x2+x2=7 (constraint 1) (constraint 2) 3x2+x2+x,210 (constraint 2) (constraint 3) X2-4 x32-8 (constraint 3) (constraint 4) x 21 and (all decision variables nonnegativel and x >0 (no nonnegativity constraint on x.i. (a) (5 pts) Convert this problem to a maximization problem with only three functional constraints, all constraints' RHS are non negative, and all decision variables need to satisfy...
samplex
Problem1: Solve the following problem using simplex method: Max. z = 2 x1 + x2 – 3x3 + 5x4 S.t. X; + 7x2 + 3x3 + 7x, 46 (1) 3x1 - x2 + x3 + 2x, 38 .(2) 2xy + 3x2 - x3 + x4 S 10 (3) E. Non-neg. x > 0, x2 > 0, X3 > 0,44 20 Problem2: Solve the following problem using big M method: Max. Z = 2x1 + x2 + 3x3 s.t. *+...
Consider the following linear program Max 3xl +2x2 S.t 1x1 + 1x2 〈 10 3x1 1x2 〈 24 1xl t 2x2< 16 And xl, x2> 0. a) Use Excel Solver to find the optimal solution to this problem. State the optimal values of xl, x2, and Z. b) Assume that the objective function coefficient for xl changes from 3 to 5. Does the optimal solution change? c) Assume that the objective function coefficient for x1 remains 3, but the objective...
Q4. (Sensitivity Analysis: Adding a new constraint) (3 marks) Consider the following LP max z= 6x1+x2 s.t.xi + x2 S5 2x1 + x2 s6 with the following final optimal Simplex tableau basis x1 r2 S2 rhs 0 0 18 0.5 0.5 0.5 0.5 x1 where sı and s2 are the slack variables in the first and second constraints, respectively (a) Please find the optimal solution if we add the new constraint 3x1 + x2 S 10 into the LP (b)...
(b) Let E = {(1, C2, C3} be the standard basis for R3, B = {bų, b2, b3} be a basis for a vector space U, and S: R3 → U be a linear transformation with the property that S(X1, X2, X3) (x2 + x3)b1 + (x1 + 3x2 + 3x3)b2 + (-3X1 - 5x2 - 4x3)b3. Find the matrix F for S relative to E and B. INSTRUCTIONS: 1. Use the green arrows next to the answer spaces below...
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