3. A company produces two products on two machines. A unit of product 1 requires 2 hours on machine 1 and 1 hour on machine 2. For product 2, a unit requires 1 hour on machine 1 and 3 hours on machine 2. The revenues per unit of products 1 and 2 are $5 and $6, respectively. The total daily processing time available for each machine is 8 hours. Letting x and y represent the daily number of units of products 1 and 2 respectively, (i)Construct the LP model to maximize profit. (ii) Obtain the optimum solution graphically by determining the number of units of each product to be produced in order to maximize the profit and at what value. (iii) If management decides to increase the daily capacity of machine 1 from

Practical Management Science
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Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
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3. A company produces two products on two machines. A unit of product 1
requires 2 hours on machine 1 and 1 hour on machine 2. For product 2, a
unit requires 1 hour on machine 1 and 3 hours on machine 2. The revenues
per unit of products 1 and 2 are $5 and $6, respectively. The total daily
processing time available for each machine is 8 hours. Letting x and
y represent the daily number of units of products 1 and 2 respectively,
(i)Construct the LP model to maximize profit.
(ii) Obtain the optimum solution graphically by determining the number of
units of each product to be produced in order to maximize the profit and
at
what value.
(iii) If management decides to increase the daily capacity of machine 1 from
8 hours to 9 hours, locate the new optimum point. Compute the dual price and
the feasibility range for machine 1.
..
Transcribed Image Text:3. A company produces two products on two machines. A unit of product 1 requires 2 hours on machine 1 and 1 hour on machine 2. For product 2, a unit requires 1 hour on machine 1 and 3 hours on machine 2. The revenues per unit of products 1 and 2 are $5 and $6, respectively. The total daily processing time available for each machine is 8 hours. Letting x and y represent the daily number of units of products 1 and 2 respectively, (i)Construct the LP model to maximize profit. (ii) Obtain the optimum solution graphically by determining the number of units of each product to be produced in order to maximize the profit and at what value. (iii) If management decides to increase the daily capacity of machine 1 from 8 hours to 9 hours, locate the new optimum point. Compute the dual price and the feasibility range for machine 1. ..
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