be the number of units allocated to supply-destination pair i (supply) and j Let Xij (demand). If we use VAM as an initialization technique, which of the following supply- destination pairs will be allocated first? Destination 1 2 3 Supply 1 15 9 13 7 Source 11 17 5 3 9. 11 9. 3 Demand 7 3 5 Activa
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- Assume the demand for a companys drug Wozac during the current year is 50,000, and assume demand will grow at 5% a year. If the company builds a plant that can produce x units of Wozac per year, it will cost 16x. Each unit of Wozac is sold for 3. Each unit of Wozac produced incurs a variable production cost of 0.20. It costs 0.40 per year to operate a unit of capacity. Determine how large a Wozac plant the company should build to maximize its expected profit over the next 10 years.Consider a toy retailer with warehouses in St. Louis and Kansas City, Missouri. The warehouses stock an identical popular toy delivered to stores in the two cities. Assume a warehouse serves only stores in its city. Weekly demand for St. Louis is normally distributed with mean 2,000, and standard deviation 400 (that is N(μ = 2,000, σ = 400)). Weekly demand for KansasCity is distributed N(μ = 2,000, σ = 300). We assume that the two cities are far enough apart so that demand in the two cities is independent.The following parameters are seen by both warehouses:Replenishment lead time in weeks ~ N(μ = 2, σ = 0.1);Fixed shipping cost of replenishment: $500;Cost per toy: $10; andHolding cost per toy 20 percent of toy’s value per year.How many toys should each location order at a time and when should they reorder if they want a 99 percent cycle service level? What if they pool the two locations?Consider again the CHB Inc. problem described in Problem 10. Suppose only a limtednumber of PPBs can be placed. CHB would like to place this limited number of PPBs incounties so that the allowable branches can reach the maximum possible population. Thefile CHBPop contains the county adjacency matrix described in Problem 10 as well as thepopulation of each county.
- A company manufactures two products. If it chargesprice pi for product i, it can sell qi units of product i,where q1 = 60 - 3p1 + p2 and q2 = 80 - 2p2 + p1. Itcosts $5 to produce a unit of product 1 and $12 to produce a unit of product 2. How many units of eachproduct should the company produce, and what pricesshould it charge, to maximize its profit? Use spreadsheet modelling in Excelwrite a linear program that will maximize profits. You don’t need to solve it. Hint: Define your variables as: Xij = tons of commodity i loaded into cargo hold jPlease show solution and formula used. Assuming the total number of students studying in the top four universities in the Philippines is approximately 158,000. And the distribution is as follows: University of the Philippines (UP) - 40% of the total number Ateneo de Manila University (ADMU) - 23,700 De La Salle University (DLSU) - 25% of the total number University of Santo Tomas - 20% of the total number And only the following number of students owns a tablet computer: 20% of UP students 85% of ADMU students 90% of DLSU students 85% of UST students What is the total market penetration of tablet computers among the students of the top four universities? What is the total market size of tablet computers in the top four universities?
- The second-largest public utility in the nation is the sole provider of elasticity in 32 counties of southern Florida. To meet the monthly demand for electricity in these counties, which is given by the inverse demand function P = 1,200 – 4Q, the utility company has set two electric generating facilities: Q1 kilowatts are produced at facility 1 and Q2 kilowatts are produced at facility 2 (so Q = Q1 + Q2). The costs of producing electricity at each facility are given by C1(Q1) = 8,000 + 6Q12 and C2(Q2) = 6,000 + 3Q22 , respectively. Determine the profit-maximizing amounts of electricity to produce at the two facilities, the optimal price, and the utility company’s profits.Leach Distributors packages and distributes industrial supplies. A standard shipment can be packaged in a class A container, a class K container, or a class T container. A single class A container yields a profit of $6; a class K container, a profit of $10; and a class T container, a profit of $8. Each shipment prepared requires a certain amount of packing material and a certain amount of time. Formulate and solve this problem using LP software. Decision variables: X1=number of class A containers to be used X2=number of class K containers to be used X3=number of class T containers to be used Resources Needed per Standard Shipment Class of Container Packing Material (pounds) Packing Time (hours) A 2 2 K 1 6 T 3 4 Total amount of resource available per week 180 pounds…Refer to the Factory-to-Six-Customers problem and start with the original information. Each customer increases demand by 1000 units. This increased demand has to be met. Re-calculate the optimal solution. At the new solution, which of the following statements is true? A. The total shipping costs are $252,900 B. Quantity shipped from Factory 1 to Customer 1 declines by 6000 units C. Both A and B D. Neither A nor
- OPEC Explain the significance of the following variables with reference to linear programming problem: Entering variable Leaving variableA retail chain has 8 stores in a region supplied from 3 supply sources. Trucks have a capacity of 25,000 units and cost $1,200 per load plus $48 per delivery. The cost of holding one unit in inventory at retail for a year is $1.5. The managers will set up milk runs from suppliers to retail stores. Assume that all trucks travel full. Suppliers are considering whether to run a milk run to 2 stores or 4 stores on each truck. Which network should be chosen if annual sales for each product at each retail store are 150,000 units?Heller Manufacturing has two production facilities that manufacture baseball gloves. Production costs at the two facilities differ because of varying labor rates, local property taxes, type of equipment, capacity, and so on. The Dayton plant has weekly costs that can be expressed as a function of the number of gloves produced TCD(X) = X2 − X + 4 where X is the weekly production volume in thousands of units and TCD(X) is the cost in thousands of dollars. The Hamilton plant's weekly production costs are given by TCH(Y) = Y2 + 2Y + 3 where Y is the weekly production volume in thousands of units and TCH(Y) is the cost in thousands of dollars. Heller Manufacturing would like to produce 9,000 gloves per week at the lowest possible cost. (a) Formulate a mathematical model that can be used to determine the optimal number of gloves to produce each week at each facility. min s.t. = 9 X, Y ≥ 0 (b) Use Excel Solver or LINGO to find the…