Solve these problems using graphical linear programming and answer the questions that follow. Use simultaneous equations to determine the optimal values of the decision variables.
a) Maximize Z = 2x1 + 10x2
b) Maximize Z = 6A + 3B (revenue)
For both questions, answer the following:
(1) |
What are the optimal values of the decision variables and Z? |
(2) |
Do any constraints have (nonzero) slack? If yes, which one(s) and how much slack does each have? |
(3) |
Do any constraints have (nonzero) surplus? If yes, which one(s) and how much surplus does each have? |
(4) |
Are any constraints redundant? If yes, which one(s)? Explain briefly. |
I want to understand the concept; please explain what is being done.
4) no constraints are redundant because, in each case all the constraints make up feasibile region and if any one of the constraints is not included, then optimal value gets affected.
Solve these problems using graphical linear programming and answer the questions that follow. Use...
Use the simplex method to solve the linear programming problem. Maximize z= 7x1 + 2x2 + x3 subject to: x1 + 4x2 + 8x3 ≤ 113 x1 + 2x2 + 10x3 ≤ 209 with x1 ≥ 0, x2 ≥ 0, x3 ≥ 0. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. A.The maximum is ___ when x1 = ___, x2 =___, and x3 = ___. (Simplify your answers.) B.There is no...
Using the information provided below, construct a linear model to maximize the profits for Puck and Pawn Company that produces hockey sticks and chess sets. Product Labor (Hr./Unit) Wood (Lb./Unit) Profit ($/Unit) Hockey Sticks (x1) 1 4 40 Chess Sets (x2) 2 3 50 Resource Availability: 40 hrs of labor per day; 120 lbs of wood Decision Variables: x1 = number of Hockey Sticks to produce; x2 = number of Chess Sets to produce Identify the Objective Function: Z =...
please Question 1 Convert the constraints into linear equations by using slack variables. Maximize z = 2X1 +8X2 Subject to:X1 + 6x2 s 15 2x1 + 9x2 s 25 X120,X220 X1 + 6x2 +51 s 15 2X1 + 9x2525 25 x1 +6X2+S1 = 15 2X1 +9x2 +52 = 25 O X1 +6X2 + 512 15 2X1 + 9x2 +522 25 X1 +6x2 = S1 +15 2x1 + 9x2 = S2 + 25 Question 2 Introduce slack variables as necessary and...
Problem 4: Sensitivity Analysis (Total 25 points) Consider the following linear program. Solve using the graphical method. A company manufactures two products, A and B. The unit revenues are $5 and $8, respectively. Two raw materials, M1 and M2 are used. The supply of M1 and M2 are 4 and 12 units, respectively. Maximize z= 5x1 + 8x2 Subject to M1 2x1 + x2 <4 3x1 + 6x2 < 12 X1, x2 > 0 M2 a) Changes in Constraint RHS...
Interpreting an LP output after solving the problem using the software. The following linear programming problem has been solved using the software. Use the output to answer the questions below. LINEAR PROGRAMMING PROBLEM: MAX 25X1+30X2+15X3 S.T. 1) 4X1+5X2+8X3<1200 2) 9X1+15X2+3X3<1500 OPTIMAL SOLUTION: Objective Function Value = 4700.000 Variable Value Reduced Costs X1 140.000 0.000 X2 0.000 10.000 X3 80.000 0.000 Constraint Slack/Surplus Dual Prices 1 0.000 1.000 2 0.000 2.333 OBJECTIVE COEFFICIENT RANGES: Variable Lower Limit Current Value Upper Limit...
Use this output to answer these questions please, I need to understand. Interpreting an LP output after solving the problem using the software. The following linear programming problem has been solved using the software. Use the output to answer the questions below LINEAR PROGRAMMING PROBLEM MAX 25x1+30x2+15x3 ST. 1) 4X1+5X2+8X3<1200 2) 9x1+15X2+3X3c1500 OPTIMAL SOLUTION: Objective Function Value- 4700.000 Variable Value 140.000 duced Costs 0.000 10.000 0.000 x1 x2 X3 0.000 80.000 Slack/Surplus 0.000 0.000 1.000 2.333 2 OBJECTIVE COEFFICIENT RANGES:...
Exercise 2 Linear Programming 1. The Scrod Manufacturing Co. produces two key items – special-purpose Widgets (W) and more generally useful Frami (F). Management wishes to determine that mix of W & F which will maximize total Profits (P). Data W F Unit profit contributions $ 30 $ 20 Demand estimates (unit/week) 250 500 Average processing rates – each product requires processing on both machines (units/hour) Machine #1 2 4 Machine #2 ...
3 Gepbab Production Company uses labor and raw material to produce three products. The resource requirements and sales price for the three products are as shown in Table 10. Currently, 60 units of raw material are available. Up to 90 hours of labor can be purchased at Sl per hour. To maximize Gepbab profits, solve the following LP: max z = 6X1 + 8X2 + 13X3 - L s.t. 3X1 + 4X2 + 6X3 - LS 0 2X1 + 2X2...