Consider the following linear programming problem:Max 9X + 8Ys.t.15(a) Use a graph to show each constraint and the feasible region.Y1018X + 5Y 9012X + 6Y ≤ 72X + Y ≤ 9OX, Y Z 051015XY1510510(c) What is the optimal value of the objective function?15XY15105(b) Identify the optimal solution point on your graph. What are the values of X and Y at the optimal solution?(x, y) =1015Y1510G O51015X4

Linear programming (LP) is a mathematical optimization technique that helps solve problems where an…

Answered: (a) Use a graph to show each constraint…

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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(b) Bowls-R-Us Company manufactures two types of bowling balls: Heavy and Light. The profit margin on a heavy ball is 30 and the profit margin on a light ball is 25. It takes 1 pound or iron ore to make a heavy ball and 0.75 pounds of iron ore to make a light ball. The cost of iron ore is $20 per pound, and the company has no more than 10 pounds of iron ore available. The company faces limited staffing which restricts total output to 19 balls. The company has pre-order for 6 heavy and 4 light balls that must be completed. (i) Calculate the maximum profit possible for Bowls-R-Us Company. (ii) If Bowls-R-Us produces only the number of balls that are pre-ordered, determine the slack in iron ore.
Consider the following linear programming model: maximize Z = 3x1 + 2x2 subject to : x1 +x2 ≤ 1 x1 + x2 ≥ 2 x1,x2 ≥ 0 a) Write this model in a standard (augmented) form. (i.e. Introduce slack/surplus, artificial etc.)b) Constract the initial simplex tableau and carry on your calculations to solve this model using the simplex method. Interpret your result.
a. What is the orrect graph that shows the feasible region for the problem. b. What are the extreme points of the feasible region? c. What is the correct graph that shows the optimal solution for the problem
Calculating outcomes as equally likely would BEST describe: O a. Maximax criterion O b. Laplace criterion O c. Regret criterion Od. Maximin criterion Determining the average payoff for each alternative and choosing the one with the BEST payoff is the approach called: ea, maximax O b. minimax regret O c. laplace Od maximin M
Q3. Solve the given LP problem on the right by using graphical solution method. a- Find the optimal solution. b- Find the optimality range for the changes in the objective coefficient c2. c- Find the feasibility range for the changes in the RHS of one of the binding constraints. (LP): Max Z = st. 2X₁ + 2X₁ + X₁ + X1, X2 ≥ 0 3X₁ + 2X₂ 2X₂ ≤ 5 X₂ ≤ 4 2X₂ ≥ 4
with the information given draw a graph, On the x-axis, you would have the number of units sold (from 0 to 800,000 in increments of 100, 000) and on the y-axis, you would have the dollar amount (from 0 to $3,200,000 in increments of $ 400,000). Draw a line from the origin with a slope equal to the variable cost per unit ($2.5) to represent total variable costs. Draw a horizontal line at $600,000 to represent total fixed costs. The sum of these two lines gives the total cost line. Draw another line from the origin with a slope equal to the selling price per unit ($4) to represent total sales. The point where the total sales line intersects the total cost line
a. Which of the following best describes the meaning of the equation P(25) = 200? 1. When 200 calculators are sold, the profit is $25. II. When 200 calculators are sold, the profit is increasing at a rate of $25 per additional calculator III. When 25 calculators are sold, the profit is $200. IV. When 25 calculators are sold, the profit is increasing at a rate of $200 per additional calculato
1. A specific assignment of values to decision variables is called what? a. Constraint b. Feasible c. Solution d. None of the above 2. Which of the following must be true of a feasible solution a. All of what Solver calls changing variables must be greater than 0 b. It is optimal c. It violates no constraints d. None of the above
FIND THE OPTIMUM SOLUTION TO X= Y= MAX Z=
b) The figure below presents an unbounded feasible region of a five constrained LP problem. 10- |(0, 6) 6. (1, 4) 4 (3, 2) 2+ (9, 0) 8 10 i. Write down in terms of x and y the inequalities that represent these constraints. ii. If the objective function is Z = 0.12x + 0.15y, determine the optimal solution to this problem (show the movement of the isocost line). ii. Identify the binding and non-binding constraints.
2 Vidhya Balan is planning to liquidate her investments in mutual funds and invest in real estate. Before making the change to her investment strategy, Vidhya wants to forecast the price of mutual funds for the next 2 months. She has collected the following data on the average fund prices for the past 10 months. Average Month Fund Price 1. 55.1 53.8 3 53.4 4 52.95 5 52.15 6. 52.75 7 52.65 8 51.5 9. 52.25 10 51.7 Using a five-period moving average, forecast the a average fund price for Period 11. b. |Using exponential smoothing with a = 0.3 forecast the average fund price for Period 11. Assume an initial forecast for Month 2 (F2) as 55.10
1. Write a linear program for the problem. 2. What is the optimal production mix among different coffee varieties and the profit associated with it? 3. What should be the per bag profit of Tarrazu which will make it beneficial to produce this variety? 4. One Cup is considering increasing the weekly bags to 150. If it costs One Cup $3.00 per bag to procure beans of any variety. Conduct sensitivity analysis and determine if One Cup should consider increasing the per week production. 5. Identify the range over which per bag profit of Sumatra and Kona may vary and still retain the current production plan as optimal for One Cup. 6. Once roasted the coffee beans must be preserved properly. To ensure that, One Cup Coffee is considering investing in a vacuum packaging machine for 24 hours/ week. It takes 10, 15 and 10 minutes to pack a bag of Sumatra, Kona and Tarazzu respectively. Identify if the current production plan will suit the installation of the new packaging scheme.

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