i) Is this a balanced problem? Why? ii) Obtain the initial feasible solution using the Northwest Corner Method. iii) Use the Stepping Stone method to determine the optimal solution from the basic feasible solution obtained in ii) above.
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- 1. True/FalseA company wants to hire 4 vendors for the sale of 4 products, they could only sell one type of product. The following table (image) indicates what each seller charges for selling each of the products. The company wants to assign each seller a product, find all possible optimal assignments by pinpointing their optimal cost. answer the following:a) It is an allocation model T() F()b) It is not a transportation model T() F()c) The model is not balanced T() F()d) The problem has exactly 24 feasible points T() F()Optimal solution 4T+3C=240 2T+1C=100 →T=30, C-40 Can you please explain to me the solution and way of how he did get the exact coordinate points in the graph? I know there is a formula or way to calculate since it is hard to find out the exact point when manually plotting a graphConsider the following LP problem: Min 6X+ 27Y Subject to : 2 X + 9Y => 25, and X + Y <= 75. Pick a suitable statement for this problem: a. X=37.5, Y=37.5 is the only optimal solution. b. Optimal Obj. function value is 75 c. X = 0, Y = 0 is the only optimal solution. d. Optimal Obj. function value is 0
- Using Excel Solve the following LP Maximize $4x + $5y Subject to 2x + 3y ≤ 20 (labor, in hours) 6x + 6y ≤ 36 (materials, in pounds) 4x + 4y ≤ 40 (storage, in square feet) x, y ≥ 0 a) Write the original optimal solution and objective function value. b) What is the optimal solution and objective function value if you acquire 2 additional pounds of material? c) What is the optimal solution and objective function value if you acquire 1.5 additional hours of labor?I will need the excel "solver" solution to be able to solve. #4) Solve the following LP Maximize $5x + $6y Subject to 2x + 3y ≤ 10 (labor, in hours) 6x + 6y ≤ 36 (materials, in pounds) 7x + 5y ≤ 40 (storage, in square feet) x, y ≥ 0 a) Write the original optimal solution and objective function value. b) What is the optimal solution and objective function value if you acquire 2 additional pounds of material? c) What is the optimal solution and objective function value if you acquire 1.5 additional hours of labor? d) What is the optimal solution and objective function value if you give up 1 hour of labor and get 1.5 pounds of material? e) What is the optimal solution and objective function value if you introduce a new product that has a profit contribution of $2? Each unit of this product will use 1 hour of labor, 1 pound of material, and 2 square feet of storage space.1. Consider the following linear programming formulation: Min 5x + 2y Subject to (1) 3x + 6y ≥ 18 (2) 5x + 4y ≥ 20 (3) 8x + 2y ≥ 16 (4) 7x + 6y ≤ 42 (5) x, y ≥ 0 a. Solve the problem graphically. Specifically, show each constraint and the feasible region, draw an objective function line and identify an optimal point (the solution). When reporting the optimal solution and the corresponding objective function value, you may estimate the optimal x and y values from the graph. b. What are the optimal values of x and y, using the solver add-in? What is the corresponding value of the objective function? c. How many extreme points does the feasible region have? Enumerate them. Hint: It's from the graph. d. Change the objective function to 15x + 12y.. What is the new optimal solution(s)?
- Solve the following LP Write the original optimal solution and objective function value. b) What is the optimal solution and objective function value if the profit for oak tables increases to $83? c) What is the optimal solution and objective function value if the profit for pine chairs decreases to $13? d) What is the optimal solution and objective function value if the profit for pine tables increases by $20? e) What is the optimal solution and objective function value if the company is required to make at least 20 pine chairs? f) What is the optimal solution and objective function value if the company is required to make no more than 55 cherry chairs?Chapter 6. Solve the following Linear Program using the Solver method and answer the questions given below (round to two decimal places): Maximize 12A + 15B s.t. 3A + 7B <= 250 5A + 2B <= 200 B <= 25 A, B >= 0 a. The optimal value of A is 31.03 and the optimal value of B is 22.41. b. The maximized function yields a solution of 708.62. Chapter 7. For the problem you solved in Q1, obtain the Sensitivity Report, and answer the following questions. Remember to round to two digits and you can enter “infinity” for unlimited regions: The range for Variable A is from ????? to ????? The range for Variable B is from ????? to ????? The range for Constraint 1 is from ????? to ????? The range for Constraint 2 is from ????? to ????? The range for Constraint 3 is from ????? to ?????develope a space matrix for macdonalds. Below are the instructions. The steps required to develop a SPACE Matrix are as follows: 1. Select a set of variables to define financial position (FP), competitive position (CP), stability position (SP), and industry position (IP). 2. Assign a numerical value ranging from +1 (worst) to +7 (best) to each of the variables that make up the FP and IP dimensions. Assign a numerical value ranging from -1 (best) to -7 (worst) to each of the variables that make up the SP and CP dimensions. On the FP and CP axes, make comparison to competitors. On the IP and SP axes, make comparison to other industries. 3. Compute an average score for FP, CP, IP, and SP by summing the values given to the variables of each dimension and then by dividing by the number of variables included in the respective dimension. 4. Plot the average scores for FP, IP, SP, and CP on the appropriate axis in the SPACE Matrix. 5. Add the two scores on the x-axis and plot the resultant…
- 1. Given the following linear programming model: Minimize Z = 480x1 + 160x2 subject to x1 + x2 >= 40 x1 + 4x2 >= 60 3x1 + x2 >= 60 x1 >= 0, x2 >= 0 a. Solve the LP model graphically and explain the solution result. b. Develop a spreadsheet model and solve using Excel Solver. What is the optimal solution? 2. Provident Capital Corp. specializes in investment portfolios designed to meet the specific risk tolerances of its clients. A client contacted Provident with P2,000,000 available to invest. Provident’s investment advisor recommends a portfolio consisting of two investment funds: the Dynamic fund and the Diversified fund. The Dynamic fund has a projected annual return of 10%, and the Diversified fund has a projected annual return of 8%. The investment advisor requires that at most P1,400,000 of the client’s funds should be invested in the Dynamic fund. Provident’s services include a risk rating for each investment alternative. The Dynamic…Please use excel for this problem A furniture manufacturer produces two types of tables – country and contemporary – using three types of machines. The time required to produce the tables on each machine is given in the following table: Machine Country Contemporary Total Machine Time Available Per Week Router 3.5 4.0 1,000 Sander 4.5 6.5 2,000 Polisher 3.0 2.0 1,500 Country tables sell for $395 and contemporary tables sell for $515. Management has determined that at least 25% of the tables made should be country and at least 38% should be contemporary. How many of each type of table should the company manufacture if it wants to maximize its revenue? Formulate an LP model for this problem Create the spreadsheet model and use Solver to solve the problem.1. Given the following linear programming model: Minimize Z = 480x1 + 160x2 subject to x1 + x2 >= 40 x1 + 4x2 >= 60 3x1 + x2 >= 60 x1 >= 0, x2 >= 0 a. Solve the LP model graphically and explain the solution result. b. Develop a spreadsheet model and solve using Excel Solver. What is the optimal solution?