Q1: Al Rabie Housewares Company produces goods A, B and C and the pro fitof Each of the mentioned products is 150, 100 and 200 dollars, respectively. TheProduction need into three raw materials M1, M2 and M3. Each unit of theproduced requires 7,4,5 units of M1 and 20,8,10 units of M2 and 20,10,15 unitsof M3 respectively. The raw materials were specified as 1200 units of materialM1, 1500 units of material M2, and 2000 units of material M3.Required: Create a mathematical model that achieves the maximum possibleprofit?

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Answered: Q1: Al Rabie Housewares Company…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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(a) During MCO, a bookstore sold 3 units of dictionaries, and 3 units of comics, and purchased 2 units of novels on day one. On day two, the bookstore purchased 3 units of novels and sold 4 units of dictionaries, and one unit of comic. On the third day, the bookstore sold 2 units of dictionaries, one unit of novel, and purchased 2 units of comic. The bookstore earned RM 100 on day one, RM 90 on day two and RM 120 on day three after the sales and purchases. Given the price of dictionary, novel, and comic are x, y. and z ringgit per unit respectively. AN, UN Write the system of linear equations. Hence, determine the prices per unit of dictionary, comic, and novel. Find the inverse matrix using Gauss-Jordan elimination method on augmented matrix. Hence, solve the system of linear equations using the inverse matrix.
B. A firm manufactures 2 product, A and B. Each product is processed by machines, M₁ and M2. Each unit of type A requires 1 hour of processing by M₁ and 2 hours in M and each unit type of type B requires 3 hours on M₁ and 1 hour on M₂. The profit on product A is P20 per unit and on product B is P30 per unit. If M₁ is available for 200 hours each month and M₂ for 300 hours, how many units of each type can be manufactured in one month in order to maximize the profits? Requirement: 1) Formulate the linear programming model 2) Solve the linear programming using the graphical method
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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.
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