a) Polokwane municipality has got three reservoirs available to supply the water needs ofthree cities. Each reservoir can supply the following liters (in thousands) of water:Reservoir 1, 2 and 3 can supply 45, 20 and 30 thousands liters respectively. The demandat city A, B and C are 35, 50 and 40 thousands liters respectively. The transportationcosts are given in Table 1.Table 1: Transportation problemCityABReservoir182894379Formulate the problem as a balanced transportation problem.

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Answered: a) Polokwane municipality has got three…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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6. The production manager for the COWRY soft drink company is considering the production of two kinds of soft drinks: regular (R) and diet (D). Two of her limited resources are production time (8 hours = 480 minutes per day) and syrup (1 of the ingredients), limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. A.What is the objective function? B. Mention all the constraints 7.Draw or solve the following graphically: Max z = 3x1 + 4x2 Xq + 2x2 s 16 2x1 + 3x25 18 X1 22 X25 10 Xq, X2 20 What are the optimal values of x4, x2, and z? s.t.
4. A body builder wants to build lean muscle using two types of supplement packets. Each packet of Brand A contains 10 grams of fat, 3 grams of carbohydrates, and 15 grams of protein. Each packet of Brand B contains 5 grams of fat, 6 grams of carbohydrates, and 30 grams of protein. He has decided that from these two types of packets, he would like to take in a maximum of 40 grams of fat per day and a minimum of 150 grams of protein per day. How many packets of each brand should he take per day to minimize the intake of carbohydrates?
need comprehensive and correct answers.This question is about optimization.
Ethan Steel, Inc. has three factories that manufacture steel components for three different rail projects located at three different sites. They want to determine how many steel components must be transported from each factory to each project site. The demand for the steel components for the three projects, A, B and C, are 2500, 3000 and 4500, respectively. The production and shipping details are as below: Production details: Factory Maximum capacity 1 3000 5000 3000 2 3 Shipping details (with per-unit shipping cost in dollars): Project Factory A B C 1 7 8 2 2 6 5 4 3 1 9 6 Develop a linear programming optimization model to determine the distribution plan (from factories to projects) that minimizes the total transportation cost. (Do NOT solve the model.)
A chemical manufacturing plant can produce z units of chemical Z given p units of chemical P and r units of chemical R, where: 2 = 40p.5 p0.5 Chemical P costs $200 a unit and chemical R costs $400 a unit. The company wants to produce as many units of chemical Z as possible with a total budget of $32,000. A) How many units each chemical (P and R) should be "purchased" to maximize production of chemical Z subject to the budgetary constraint? Units of chemical P, p = Units of chemical R, r = B) What is the maximum number of units of chemical Z under the given budgetary conditions? (Round your answer to the nearest whole unit.) Max production, z= units
Problem Il: A company plans to make 3 models (A, B, and C) of their main product next month. Production capacity is limited to 100 totals. Each model takes the same about of production time. A supplier problem results in only 1,000 gallons being available next month. Each Model A requires 5 gallons of paint, each Model B requires 7 gallons and each Model C requires 10 Ballons. Marketing wants the following mix: at least 5 Model B's; and no more than 2 Model C's for each Model B produced. The firm wants to select that product mix so as to maximize profit contribution. Here are the numbers that go into profit contribution: Product profit per unit A 1600 $ 1500 $ B 1200 S Formulate this as a linear programming problem.
b4 provide handwritten answer
A company uses four special tank trucks to deliver four different gasoline products to customers. Eachtank has five compartments with capacities: 500, 750, 1200, 1500, and 1750 gallons. The daily demands forthe four products are 10000, 15000, 12000, and 8000 gallons. Any quantities that cannot be delivered by thecompany’s four trucks must be subcontracted at the additional costs of 5, 12, 8, and 10 cents per gallon forproducts 1, 2, 3, and 4, respectively. The goal is to develop the optimal daily loading schedule for the fourtrucks that will minimize the additional cost of subcontracting. Formulate this problem as an integer linearprogram, and solve it using linear program solver.
i. What is the total cost?
Hoosier Power needs to determine a capacity expansion plan to meet Bloomington’s power needs for thenext 20 years. The current capacity is 5000 kwh. The demand for the current year is 4000 kwh, and demand is expected to increase by 1000 kwh in each succeeding year. At the beginning of each year, Hoosier Power must determine the amount of capacity to add, given the following inputs: ■ Any year in which capacity is added, a fixed cost of $120,000 is incurred plus a cost of $120 per kwh of capacity. ■ At most 10,000 kwh of capacity can be added in a single year. ■ It costs $25 per year to maintain a unit of capacity. ■ It costs $12 per year to produce a kwh. ■ If production does not meet demand, a shortage cost of $80 per kwh short is incurred. Develop a linear integer model to help Hoosier Power minimize its costs for the next 20 years.

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