(a) Formulate a linear programming model to determine the optimal product mix that will maximize profit. (b) Solve Problem graphically. (c) Transform this model into standard form. (d) Identify the amount of unused resources (i.e., slack) at each of the graphical extreme points. (e) What would be the effect on the optimal solution if the production time on line 1 was reduced to 4o hours? (f) What would be the effect on the optimal solution if the profit for product B was increased from $7 to $15? to $20?

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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PLEASE SOLVE THE FOLLOWING PARTS OF THIS QUESTION IN THE IMAGE.

d) Identify the amount of unused resources (i.e., slack) at ach of the graphical extreme points.

e) What would be the effect on the optimal solution if the production time on line 1 was reduced to 40 hours?

f) What would be the effect on the optimal solution if the profit for product B was increased from $7 to $15? to $20?

Assignment 1
• A company produces two products A and B, which
have profits of $9 and $7, respectively. Each unit of
product must be processed on two assembly lines,
where the required production times are as follows
Hours/Unit
Product
Line 2
Line 1
A
12
B
4
Total hours
60
40
Assignment 1 Con't
77
(a) Formulate a linear programming model to determine
the optimal product mix that will maximize profit.
(b) Solve Problem graphically.
(c) Transform this model into standard form.
(d) Identify the amount of unused resources (i.e., slack) at
each of the graphical extreme points.
(e) What would be the effect on the optimal solution if the
production time on line 1 was reduced to 4o hours?
(f) What would be the effect on the optimal solution if the
profit for product B was increased from $7 to $15? to $20?
Transcribed Image Text:Assignment 1 • A company produces two products A and B, which have profits of $9 and $7, respectively. Each unit of product must be processed on two assembly lines, where the required production times are as follows Hours/Unit Product Line 2 Line 1 A 12 B 4 Total hours 60 40 Assignment 1 Con't 77 (a) Formulate a linear programming model to determine the optimal product mix that will maximize profit. (b) Solve Problem graphically. (c) Transform this model into standard form. (d) Identify the amount of unused resources (i.e., slack) at each of the graphical extreme points. (e) What would be the effect on the optimal solution if the production time on line 1 was reduced to 4o hours? (f) What would be the effect on the optimal solution if the profit for product B was increased from $7 to $15? to $20?
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