Show your complee solution to each of the following problems:1. A washing machine manufacturing company has two supply sources A, and B withcapacities of 60 and 70 units respectively. The company needs to transport washingmachines to its destribution centers at Laguna (L), Batangas (B), and Cavite (C)with demands of 30, 40, and 60 units respectively. The cost of transporting 1unit of washing machine from one source to a certain destination is given in thefollowing table:source destinationABDemandL BP 30P 6030assignment employeeJob 1Job 2Job 3Job 4Job 5Find the number of units to be transported from each source to each distributioncenter that gives the minimum total transportation cost.P40P 20402. In a department store, there are five newly hired employees A, B, C, D, E ad fivejobs 1, 2, 3, 4, 5. Assigning a job to a certain employee will cost the owner to paythat employee a monthly salary shown in he table below.A BP 20kP18kP21kP 17kP 18kCP 30P 15kP 20kP23kP8060P 18kP 18kSupply6070DEP25kP 15kP25kP 20kP20kCP 18kP20kP12kP 14kP25kP27kP21kP23kP 16k P 19kHow should the store owner assign the available jobs to his employees so that itwill cost him as little as possible to pay all his employees per month?

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Answered: 1. A washing machine manufacturing…

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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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?
French Biscuit Manufacturer (FBM), produces two types of biscuits (1) double chocolate biscuits and (ii) tea time biscuits in two separate manufacturing units. They are interested in expanding the manufacturing units (one by one) because there is a demand in the market but facing a difficulty to decide which manufacturing unit should expand first. Company officials decided that the expansion decision was based upon monthly demand. FBM official consults you and requests to give your valuable suggestion which will be helpful for final decision. you analyzed the following normally distributed data: Monthly Sale of Biscuits Double 8551 6314 5259 8138 8429 4807 8025 6845 6478 7513 Chocolate 9125 4894 9106 8775 10070 7845 6229 8459 10542 4190
8. A person on a high-protein, low-carbohydrate diet requires at least 100 units of protein and at most 24 units of carbohydrates daily. The diet will consist entirely of three special liquid diet foods: A, B, and C. The contents and costs of the diet foods are given in the table. How many bottles of each brand of diet food should be consumed daily in order to meet the protein and carbohydrate requirements at minimal cost? What is the minimum cost? Note: Use the big M method. Protein Carbohydrates Units per bottle A 10 2 Cost per bottle ($) 0.60 B 10 3 0.40 C 20 4 1.50
Q1) A company manufactures two products (pl and p2) on three machines (ml, m2 and m3). Each of the products must be processed on all three machines. One unit of pl requires 5h (hours) of processing time on ml, 4h of processing time on m2 and 3h processing time on m3. Machining times required by a unit production of p2 are 2h, 3h and 4h respectively. The machine capacities are 270h, 250h, and 200h per pieces respectively. The unit profits for the products are $100 and $60 respectively. Additionally the manufacturer wants to produce at least five pl for each p2. Suppose that the produced each product is sold. Formulate a Linear Programming (LP) Model to determine the number of pl and p2 that maximize the overall profit. (Define the decision variables. Write the objective function, and the constraints. Indicate sign restrictions. Do not try to solve the problem.)
A manufacturing firm has four factories from which product is shipped to three warehouse for onward distribution to stores. The following table reports a partial shipment plan to meet demand. The partial shipment plan, the total supplies at the factories and the required demands at the warehouses are reported in the table below. Factory Warehouse A Warehouse B Warehouse C Supply Factory 1 70 210 100 380 Factory 2 110 90 Answer 278 Factory 3 200 110 220 530 Factory 4 120 90 80 290 Demand 500 500 478 For the above shipment plan to be feasible, what is the number of units shipped from Factory 2 to Warehouse C? Report the number within the table.
1. ARI Chemicals produces two products that are sold as raw materials to companies manufacturing bath soaps and laundry detergents. Based on an analysis of current inventory levels and potential demands for the coming month, ARI management specified that the combined production for products A and B must total at least 350 gallons. Separately, a major customer’s order of 125 gallons of product A must also be satisfied. Product A requires 2 hours of processing time per gallon and product B requires 1 hour of processing time per gallon. For the coming month, 600 hours of processing time are available. ARI's objective is to satisfy these requirements at a minimum total production cost. Production costs are $2 per gallon for product A and $3 per gallon for product B. - Generate the mathematical model for the optimal number of products A and B to be produced by ARI chemicals. - Create Graph
Find the first 5 terms of the solution: (x+2)y' - 3y = 1+x+x² ; Xo=0
Tri-County Utilities, Inc., supplies natural gas to customers in a three-county area. The company purchases natural gas from two companies: Southern Gas and Northwest Gas. Demand forecasts for the coming winter season are as follows: Hamilton County, 400 units; Butler County, 200 units; and Clermont County, 300 units. Contracts to provide the following quantities have been written: Southern Gas, 500 units; and Northwest Gas, 400 units. Distribution costs for the counties vary, depending upon the location of the suppliers. The distribution costs per unit (in thousands of dollars) are as follows:
The Ace Manufacturing Company has orders for three similar products. Orders (units) 2,200 Product A B C с 1 2 Machine 3 Three machines are available for the manufacturing operations. All three machines can produce all the products at the same production rate. However, due to varying defect percentages of each product on each machine, the unit costs of the products vary depending on the machine used. Machine capacities for the next week and the unit costs are shown below. A A B B C с Product 1 2 3 300 1,400 Capacity (units) 1,800 1,700 800 1 Machine 2 3 $1.00 $1.30 $1.10 $1.20 $1.40 $1.00 $0.90 $1.20 $1.20
Consider a two country world producing only meat and potatoes. If the world equilibrium relative price of potatoes is between 1 5 and 1 3 pounds of meat, then the world equilibrium relative price of meat: a) will lie between 1 and 1 3 pounds of potatoes as well. b) must lie between 3 and 5 pounds of potatoes. c) cannot be determined without additional data
A factory works 8 hours a day, producing three products namely A, B and C. each of these products is processed in three different operations namely 1, 2 and 3. The processing times in minutes for each of these products in each of the operations are given below along with utilization of the processes and the cost and price in kwachas for each of these three products which have unlimited demand. Product Processing time (mins) in operation Cost/unit Price/unit 1 3 (K) (K) 1 10 16 2 1 4 10 Utilisation 80% 70% 90% Formulate a linear programming model for this problem Detemine the optimal product mix using the simplex method. iii. Give the interpretations for the values obtained in the final simplex table 529 ABC

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