A manufacturer has two factories, located in Toronto and Winnipeg. Warehouses are located in Moncton,Montreal, and Calgary. Minimum requirements at the three warehouses are for at least 5 000, 8 000, and7 000 units, respectively. The production capacities of the two factories are 9 000 and 11 000 units,respectively. Shipping costs per unit from each factory to each warehouse are given below:FACTORYMonctonTorontoWAREHOUSE$14$22$6Winnipeg$17The manufacturer wants to determine the optimal shipping schedule that will minimize transportationcosts. Formulate the linear programming model for this problem.MontrealCalgary$18$9

Given:MonctonMontrealCalgaryToronto$14$6$18Winnipeg$22$17$9To Do: Formulate that will minimize…

Answered: A manufacturer has two factories,…

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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A small machine shop has one drilling and five milling machines, which are to be used to produce a finished product consisting of two parts, P1 and P2. The productivity of each machine for the two parts is given below: Production Time (Minutes per Piece) Part Profit ($ per Piece) Drilling Milling P1 4 3 20 P2 5 15 It is desired to maintain a balanced loading on all machines such that no machine runs for more than 30 min per day longer than any other machine (assume that the milling load is split evenly among all five milling machines). Formulate a linear program to divide the work time of each machine to maximize the profit assuming an 8 h working day.
There are three factories located at AR, IN, and TX respectively. From these locations, a certain commodity is to be delivered to each of the two warehouses situated at A and B. The revenue per commodity item is $10. The weekly demand of the warehouse A and B are respectively 50 and 35 units of the commodity while the production capacity of the factories at AR, IN, and TX are respectively 28, 22, and 35 units. The cost of transportation per unit is given as belows. Cost Warehouse A Warehouse B AR 5 3 IN 6 6 TX 2 4 To maintain a good relationship with all the factories, warehouse B requires that it receives at least 40% of its product from factory in TX. Realize that it is making good profit in warehouse A, AR requires that at least 35% of its product shipped to warehouse A. Formulate (without solving) a linear programming problem to maximize the profit.
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:
A chicken farmer can buy a special food mix A at 20c per Kg and special food mix B at 40c perKg. Each Kg of mix A contains 3000 units of nutrient N1 and 1000 units of nutrient N2; eachKg of mix B contains 4000 units of nutrient N1 and 4000 units of nutrient N2. If the minimumdaily requirements for the chickens collectively are 36000 units of nutrient N1 and 20000 unitsof nutrient N2, how many pounds of each food mix should be used each day to minimize dailyfood costs while meeting (or exceeding) the minimum daily nutrient requirements? What is theminimum daily cost?
Bexter Labs produces three products: A, B, and C.Bexter can sell up to 2000 units of product A, up to 3000 units of product B, and up to 5000 units of prod-uct C. Each unit of product C uses two units of A and three units of B and incurs $7 in processing costs. Prod-ucts A and B are produced from either raw material 1 or raw material 2. It costs $9 to purchase and process one unit of raw material 1. Each processed unit of raw mate-rial 1 yields two units of A and four units of B. It costs $5 to purchase and process a unit of raw material 2.Each processed unit of raw material 2 yields one unit ofA and three units of B. The unit prices for the products are: A, $10; B, $9; and C, $32. The quality levels ofeach product are: A, 7; B, 9; and C, 6. The average quality level of the units sold must be at least 8. Deter-mine how to maximize Bexter’s profit.

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