(i)Construct the LP model to maximize profit. 3 (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 4 hours to 5 hours, locate the new optimum point. Compute and comment on the dual price and the feasibility range for machine 1. (iv) If management decides to increase the daily capacity of machine 2 from 5 hours to 6 hours, locate the new optimum point. Compute and comment on the dual price and the feasibility range for machine 2.

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter12: Queueing Models
Section12.3: The Exponential Distribution
Problem 3P
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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 2 hours on machine 2. The revenues per unit
of products 1 and 2 are $2 and $3, respectively. The total daily processing time
available for machine 1 and 2 are 4 and 5 hours respectively. Letting x, and
x2 represent the daily number of units of products 1 and 2 respectivelv.
(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
4 hours to 5 hours, locate the new optimum point. Compute and comment on
the dual price and the feasibility range for machine 1.
(iv) If management decides to increase the daily capacity of machine 2
from 5 hours to 6 hours, locate the new optimum point. Compute and
comment on the dual price and the feasibility range for machine 2.
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 2 hours on machine 2. The revenues per unit of products 1 and 2 are $2 and $3, respectively. The total daily processing time available for machine 1 and 2 are 4 and 5 hours respectively. Letting x, and x2 represent the daily number of units of products 1 and 2 respectivelv. (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 4 hours to 5 hours, locate the new optimum point. Compute and comment on the dual price and the feasibility range for machine 1. (iv) If management decides to increase the daily capacity of machine 2 from 5 hours to 6 hours, locate the new optimum point. Compute and comment on the dual price and the feasibility range for machine 2.
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ISBN:
9781337406659
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Cengage,