How are mathematical models helpful in determining the objective function & constraints equations in a linear programming problem?
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How are mathematical models helpful in determining the objective function & constraints equations in a linear programming problem?
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- Please show how to solve bLinear programming model formulation. Data Decision variables Objectives ConstraintsTimely Transport provides local delivery service for a number of downtown and suburban businesses. Delivery charges are based on distance and weight involved for each delivery: 10 cents per pound and 15 cents per mile. Also, there is a $10 handling fee per parcel.a. Develop an expression that summarizes delivery charges.b. Determine the delivery charge for transporting a 40-pound parcel 26 miles.
- A manufacturing firm closed down the production of a certain unprofitable product line.This necessitated the rational utilization of released excess production capacity.Management has been contemplating to devote this excess capacity to the manufacture of one or more of the three products A, B and C. The details about available excess machine capacity and machine requirements for the various products are given in I and II.I. Machine Type Available access Machine Time Milling Machine 250 hours / week Lathe 150 hours /week Ginder 50 hours /week II. Machine Type Machine hour requirements per unit of product A B C Milling Machine 8 2 3 Lathe 4 3 0 Ginder 2 0 1 It was assumed that the unit profit would be $20, $6 and$8 respectively, for products A, B and C. i. Formulate the L.P. problemii. Solve the problem by simplex methodChapter : sensitivity analysis in linear programmingProblem 6-09 (Algorithmic) The Ace Manufacturing Company has orders for three similar products: Product Order (Units) A 1750 B 500 C 1100 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 as follows: Machine Capacity (Units) 1 1550 2 1450 3 1150 Product Machine A B C 1 $0.80 $1.30 $0.70 2 $1.40 $1.30 $1.50 3 $0.80 $0.80 $1.20 Use the transportation model to develop the minimum cost production schedule for the products and machines. Show the linear programming formulation. If the constant is "1" it must be entered in the box. If your answer is zero enter "0". The linear programming formulation and optimal solution are shown. Let xij = Units of…
- Problem 4-11 (Algorithmic) Edwards Manufacturing Company purchases two component parts from three different suppliers. The suppliers have limited capacity, and no one supplier can meet all the company’s needs. In addition, the suppliers charge different prices for the components. Component price data (in price per unit) are as follows: Supplier Component 1 2 3 1 $11 $12 $13 2 $9 $10 $9 Each supplier has a limited capacity in terms of the total number of components it can supply. However, as long as Edwards provides sufficient advance orders, each supplier can devote its capacity to component 1, component 2, or any combination of the two components, if the total number of units ordered is within its capacity. Supplier capacities are as follows: Supplier 1 2 3 Capacity 500 900 700 If the Edwards production plan for the next period includes 900 units of component 1 and 700 units of component 2, what purchases do you recommend? That is, how many units of each…Question Primer Inc. offers plumbing and air conditioning services to customers in Kumasi, Ghana. The company’s product strategy is to solve the customer’s problem irrespective of what it takes, at the time the customer needs it solved. The company provides same day service for customers, and theaim is to make the customer happy before leaving.The services of the company are available 24 hours a day, 7 days a week for customers. There is no extra charge for requests made on holidays, odd hours of the day, or in festive seasons. The company aims to be available at the call of customers without charging a pesewa extra, even at times when rival firms won’t get out of bed. The company fixes the price of the service before it begins, and customers can be assured of no extra charges. Irrespective of the customer’s location in the city, Primer Inc. does not charge additional fees for transportation. For all services, the company provides a one year guarantee on all parts and labour used,…Q2 The lower daily needs for workers in a manufacturing organization provided in the below table, each worker works for eight hours, the management needs to determine the lower number of workers to maintain the flow and stability of the work in each shaft. Formulate LP model for this problem and suggest (only suggestion) a method to find the optimal solution Shaft
- Define Linear programming (LP)?#5) Solve the following LP a) Write the original optimal solution and objective function value. b) What is the optimal solution and objective function value if the profit for oak tables increases to $83? c) What is the optimal solution and objective function value if the profit for pine chairs decreases to $13? d) What is the optimal solution and objective function value if the profit for pine tables increases by $20? e) What is the optimal solution and objective function value if the company is required to make at least 20 pine chairs? f) What is the optimal solution and objective function value if the company is required to make no more than 55 cherry chairs?Problem 3-19 (Algorithmic) Better Products, Inc., manufactures three products on two machines. In a typical week, 40 hours are available on each machine. The profit contribution and production time in hours per unit are as follows: Category Profit/unit Machine 1 time/unit Machine 2 time/unit Product 1 2 3 Two operators are required for machine 1; thus, 2 hours of labor must be scheduled for each hour of machine 1 time. Only one operator is required for machine 2. A maximum of 90 labor-hours is available for assignment to the machines during the coming week. Other production requirements are that product 1 cannot account for more than 50% of the units produced and that product 3 must account for at least 10% of the units produced. a. How many units of each product should be produced to maximize the total profit contribution? If required, round your answers the nearest whole number. If your answer is zero, enter "0". Profit = $ $ Machine 2 What is the projected weekly profit associated…