V₁ V₂ V3 Supply 5 3 1 U₁ 10 2 3 4 20 112 4 2 30 U3 Demand 15 20 25 A) Find a basic feasible solution, by using - Northwest corner method. B) Check if the initial solution is optimal if not find it, by using method of multipliers
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- A manufacturer produces two types of calculator; each requiring material and labour as shown below: Input Scientific Calculator Graphic Calculator Availability Labour (hrs) 4 5 200 Inspection time 2 1 80 Material (cm2) 10 12 600 PROFIT $200 $300 Write the objective function and he constraints Diagram the constraint and identify the feasible region Using the corner point method, identify the production level that meets the objective of maximum profitAssuming that the company is interested in maximizing the total profit contribution, answer the following: A, What is the linear programming model for this problem? Decision Variables: LP Model: B.Find the optimal solution using the graphical solution procedure. 1.Feasible Region:2. Identify the binding constraint/s:3. Identify the rebundant constraint/s:4.How many gloves of each model should Kelson manufacture?5.What is the total profit contribution Kelson can earn with the given production quantities? C.How many hours of production time will be scheduled in each department? D.What is the slack time in each department? E.Compute the range of optimality for the objective function coefficientsBased on the following sensitivity analysis, which of the following products would be considered most sensitive to changes or errors in the objective function coefficient? Variable Cells Cell Name Final Value Reduced Cost Objective Coefficient AllowableIncrease AllowableDecrease $B$2 Product_1 0 −2 25 10 5 $B$3 Product_2 175 0 25 10 14 $B$4 Product_3 0 −1.5 25 8 6 Constraints Cell Name Final Value Shadow Price Constraint R.H.Side AllowableIncrease AllowableDecrease $H$9 Resource_A 0 0 100 1E+30 100 $H$10 Resource_B 525 0 800 1E+30 275 $H$11 Resource_C 700 1.75 700 366.6666667 700 Choose the product Product 1 Product 2 Product 3
- Based on the following sensitivity analysis, which of the following products would be considered most sensitive to changes or errors in the objective function coefficient? Variable Cells Cell Name Final Value Reduced Cost Objective Coefficient AllowableIncrease AllowableDecrease $B$2 Product_1 0 −2 25 11 4 $B$3 Product_2 175 0 25 12 14 $B$4 Product_3 0 −1.5 25 8 5 Constraints Cell Name Final Value Shadow Price Constraint R.H.Side AllowableIncrease AllowableDecrease $H$9 Resource_A 0 0 100 1E+30 100 $H$10 Resource_B 525 0 800 1E+30 275 $H$11 Resource_C 700 1.75 700 366.6666667 700 multiple choice Product_1 Product_2 Product_3Consider a monopolistically competitive market with NN firms. Each firm's business opportunities are described by the following equations: Demand: Q=100N−PQ=100N−P Marginal Revenue: MR=100N−2QMR=100N−2Q Total Cost: TC=50+Q2TC=50+Q2 Marginal Cost: MC=2QMC=2Q How much profit does each firm make? a: 1,250/N*2−50 b: 2,500/N*2−50 c: 50+625/N*2 d: 1,875/N*2 In the long run, how many firms will exist in this market?Modify the warehouse location model as suggested inModeling Issue 2. Specifically, assume that the samefour customers have the same annual shipments, butnow, there are only two possible warehouse locations,each with distances to the various customers. (Thesedistances, along with other inputs, are in the fileP07_27.xlsx.) The company can build either or bothof these warehouses. The cost to build a warehouseis $50,000. (You can assume that this cost has beenannualized. That is, the company incurs a buildingcost that is equivalent to $50,000 per year.) If onlyone warehouse is built, it will ship to all customers. However, if both warehouses are built, then the com-pany must decide which warehouse will ship to each customer. There is a traveling cost of $1 per mile.a. Develop an appropriate model to minimize totalannual cost, and then use Solver to optimize it.Is this model an NLP or an IP model (or both)?b. Use SolverTable with a single input, the traveling costper mile, to see how large…
- A manager must make a decision on shipping. There are two shippers, A and B. Both offer a twoday rate: A for $500 and B for $525. In addition, A offers a three-day rate of $460 and a nine-dayrate of $400, and B offers a four-day rate of $450 and a seven-day rate of $410. Annual holdingcosts are 35 percent of unit price. Three hundred boxes are to be shipped, and each box has a priceof $140. Which shipping alternative would you recommend? Explain.7. The airline offering the flights and fares shown in Table 8.4 decides to raise the SanFrancisco–to–St. Louis discount fare from $170 to $225. It estimates that discount demand atthis new fare will be 20. Given that all other fares and demands remain the same, determine thenew optimal set of allocations and total revenue for the network using linear programming.Consider the following linear program: Max 3A + 3B S.t. 2A + 4B < 12 6A + 4B < 24 A, B > 0 Find the Optimal Solution using the graphical solution procedure If the objective function is changed to 2A + 6B, what will the optimal solution be? How many extreme points are there? What are the values of A and B at each extreme point?
- [6] Please carefully read the following scenario:(Image attached)The total number of decision variables in this problem is:A. 5B. 3C. 4D. 2 [7] The total number of constraints in this problem, including non-negativity constraints is: A. 9 B. 5 C. 3D. 7Road Runner Co is a Pakistani manufacturer making Bicycles. It exports to two markets, Bangladesh and Sri Lanka. Demand for Bicycles in these two markets is given by the following Functions: Bangladesh Q1 = 12 – P1 Sri Lanka Q2 = 8 – P2 Where Q1 and Q2 are respective quantities sold (in thousands) andP1 and P2 are the respective prices (in Pak. Rupees per unit) in the two markets. Total cost function is C = 5 + 2 (Q1+ Q2) a) Determine the company’s total profit function. Also, (i) What are the profit maximizing levels of price and output for the two markets? (ii) Calculate the marginal revenues in each market. b) Now consider two cases: (i) Company is effectively able to price discriminate in the two markets. What will be the total profits? (ii) Suppose the company does not engage in price discrimination. By charging the same price in the two markets what are the profit maximizing levels of price, output, and the total profits?…3-2) The optimal quantity of the three products and resulting revenue for Taco Loco is: A) 28 beef, 80 cheese, and 39.27 beans for $147.27. B) 10.22 beef, 5.33 cheese, and 28.73 beans for $147.27. C) 1.45 Z, 8.36 Y, and 0 Z for $129.09. D) 14 Z, 13 Y, and 17 X for $9.81. 3-3) Taco Loco is unsure whether the amount of beef that their computer thinks is in inventory is correct. What is the range in values for beef inventory that would not affect the optimal product mix? A) 26 to 38.22 pounds B) 27.55 to 28.45 pounds C) 17.78 to 30 pounds D) 12.22 to 28 pounds