1. A state has three power plants with generating capacities of 30, 40 and 25 million KWH that supply electricity to three cities located in the same state. The demand requirements (maximum) of the three cities are 35, 40 and 20 million KWH. The distribution cost (Rs. in thousand) per million unit for the three cities are given in the table below: City 1 2 3 60 75 45 Plant 2 35 35 40 3 55 50 45 a. Formulate the problem as a transportation model. b. Determine an economical distribution plan. If the demand is estimated to increase by 15%, what is your revised plan? d. If the transmission loss of 5% is considered, determine the optimal plan.
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- This problem is based on Motorolas online method for choosing suppliers. Suppose Motorola solicits bids from five suppliers for eight products. The list price for each product and the quantity of each product that Motorola needs to purchase during the next year are listed in the file P06_93.xlsx. Each supplier has submitted the percentage discount it will offer on each product. These percentages are also listed in the file. For example, supplier 1 offers a 7% discount on product 1 and a 30% discount on product 2. The following considerations also apply: There is an administrative cost of 5000 associated with setting up a suppliers account. For example, if Motorola uses three suppliers, it incurs an administrative cost of 15,000. To ensure reliability, no supplier can supply more than 80% of Motorolas demand for any product. A supplier must supply an integer amount of each product it supplies. Develop a linear integer model to help Motorola minimize the sum of its purchase and administrative costs.Consider the following linear programming problem: Min Z = 50x1 + 60x2 s.t. 6x1 + 5x2 >= 30 8x1+4x2 >= 32 x1,x2 >=0. What is the Z in the optimal point of this problem? a. 200 b. 250 c. 300 d. 350 e. none of the abovThe following table shows the amount spent by four U.S. airlines to fly one available seat 1 mile in the second quarter of 2014. Set up a system and then solve using technology. Airline United Continental American JetBlue Southwest Cost 14.9 14.6 11.9 12.4 Suppose that, on a 3,000 - mile New York to Los Angeles flight, United Continental, American, and Southwest flew a total of 240 empty seats, costing them a total of $100,920. If United Continental had three times as many empty seats as American, how many empty seats did each of these airlines carry on its flight? United Continental empty seats American empty seats Southwest empty seats
- A goldsmith makes two types of jewelry. A model A ring is made with 1 g of gold and 1.5 g of silver and sells for 25 UM.Another model B ring sells for 30 UM and is made of 1.5 g of gold and 1 g of silver. If you only have 750 gof each metal, how many rings should be made of each type to obtain maximum profit?Requested:- Make Initial Table of the problem.- Obtain the Case Variables- Obtain the Objective Function- Get Restrictions- Create the Simplex Table- Obtain the Optimal Solution and the Slack Variables.Solve this operational research exercise.A decision problem has the following three constraints: 70X + 6Y <= 420; 24X + 3Y= 72; and 11X - Y <= 14 . The objective function is Min 17X + 38Y . The objective function value is : a. 338 b. 676 c. unbounded d. infeasible e. 0Consider a small Oil production firm with 5 competing oil production projects, A - E. The table below shows the estimated long-term profit (Net Present Value) for each project as well as the amount of investment capital required to start the project. You have been contacted to help select the best combination of projects to maximize the Net Present Value subject to the capital investment limit of $32 million. Production Project A B C D E Estimated Profit (millions) 25 20 19 28 21 Capital Required (millions) 11 8 14 19 13 Formulate a Binary Integer Programming (BIP) model on a spreadsheet. Solver the model using Solver.
- 1. (i) A consumer has income of £3,000. Apple juice is priced at £3 a bottle and cheese is priced at £6 a kilo. Drawthe budget constraint for a consumer with standard preferences. What is the slope of this budget constraint? (ii) Show a consumer’s budget constraint and indifference curves for apple juice and cheese. Show the optimalconsumption choice. If the price of juice is £3 a bottle and the price of cheese is £6 a kilo, what is the marginalrate of substitution at this optimum? (iii) The price of cheese rises from £6 to £10 a kilo, while the price of juice remains at £3 a bottle. For aconsumer with a constant income of £3,000, show what happens to consumption of juice and cheese.Decompose the change into income and substitution effects.Asilekpe Company Limited is considering constructing a borehole in the village of Adukofe. The construction would cost Gh₵2 million and there will be no cost of maintenance. The following table shows the company’s anticipated demand over the lifetime of the bridge: Price per gallon (Gh₵) Number of gallons 8 0 7 100000 6 200000 5 300000 4 400000 3 500000 2 600000 1 700000 0 800000 a. If the company were to construct the borehole what would be its profit-maximizing price? Would that be the efficient level of output? Explain your answer.b. If the company is interested in maximizing profit, should it construct the borehole? What would be its profit or loss?c. If the government were to construct the borehole, what price should it charge? d. Should the government construct the borehole? Explain.Only Construct Linear Programming Model for the following Problemb; An individual wishes to invest $9000 over the next year in two typar of inventrent linvestment A yinlds 5% and invertment � yields 8%. Market retearch rocotnenends an allocs tion of at least 25% in A and at most 30% in �. Motsover, investment in A should be at least ball the invertmeut in �. How should the fund be allocated to the two imetrinents?
- Mo. Samsung produces semiconductor chips in South Korea, China, and the United States. Products using these chips are sold around the world and therefore Samsung sells them on every continent. Below is the available supply and demand for all locations with the associated shipping costs. Supply (in millions) Demand (in millions) South Korea – 2.5 China – 3.5 United States – 2.0 North America – 2.1 South America – 1.4 Europe – 1.2 Africa – 1.1 Asia – 2.3 Australia – 0.8 Shipping Costs North America South America Europe Africa Asia Australia South Korea $12 $14 $9 $7 $3 $13 China N/A $15 $10 $8 $5 $16 United States $4 $6 $11 $17 N/A $18 Ongoing trade tensions between the United States and China have resulted in a ban on imports/exports. Additionally, the United States can only supply North America with 1.5 million and Australia requires at least 500,000 from South Korea. Using all this information, determine the optimal solution to the problem.Given this linear programming model, solve the model and then answer the questions that follow.Maximize Z = 12x1 + 18x2 + 15x3 where x1 = the quantity of product 1 to make, etc.Subject toMachine 5x1 + 4x2 + 3x3 ≤ 160 minutes Labor 4x1 + 10x2 + 4x3 ≤ 288 hoursMaterials 2x1 + 2x2 + 4x3 ≤ 200 poundsProduct 2 x2 ≤ 16 units x1, x2, x3 ≥ 0 a. Are any constraints binding? If so, which one(s)?What combination of x and y will yield the optimum for this problem? Maximize $10x + $4y, subject to (1) 5x + 3y ≤ 15 and (2) 3x + 6y ≤ 18 and (3) x, y ≥ 0.