Answer The Survey Quations
It is important that I learn from you regarding the course materials (synchronous lectures, asynchronous lectures, handouts, examples, etc.) we covered in past sessions. With that in mind, I have designed the following questionnaire. I will appreciate your feedback by 11:59 pm on Sunday (October 4). If you answered “No” to a question, pleased don’t answer the follow up questions pertaining to that question to maintain the integrity of your responses. It is important that you complete viewing the asynchronous lecture assuming that you have attended the Synchronous class held on September 30. Participating in the survey will count toward your participation points.
Q-6- what would you like to learn more in reference to the synchronous lecture?
Q-if you present ,what did you learn that you did not learn before ?
Q- if you complete listening to. th synchronous lecture ,what did you learn you did not learn prior to this class?
Chapter 3: Solutions to Practice
Problem
12. x1 = no. of days to operate Mill 1
x2 = no. of days to operate Mill 2
minimize Z = 6,000×1 + 7,000×2 subject to
6×1 + 2×2 ≥ 12
2×1 + 2×2 ≥ 8
4×1 + 10×2 ≥ 5
x1,x2 ≥ 0
16.
a) x1 = 320, x2 = 90
320 + 90 + s1 = 410
s1 = 0 acres uncultivated
90 + s3 = 100
s3 = 10 acres of tobacco
allotment unused
b) At point D only corn is planted. In order for
point D to be optimal the slope of the
objective function will have to be at least as
great (i.e., steep) as the slope of the constraint
line, x1 + x2 = 410, which is −1. Thus, the
profit for corn is computed as,
−c1/520 = −1
c1 = 520
The profit for corn must be greater than $520 for
the Bradleys to plant only corn.
c) If the constraint line changes from x1 + x2 =
410 to x1 + x2 = 510, it will move outward to a
location which changes the solution to the
point where 105×1 + 210×2 = 52,500 intersects
with the axis. This new point is x1 = 500, x2 =
0, Z = $150,000.
d) If the constraint line changes from x1 +
x2 = 410 to x1 + x2 = 360, it moves inward to a
location which changes the solution point to
the intersection of x1 + x2 = 360 and 105×1 +
210×2 = 52,500. At this point x1 = 260, x2 =
100, and Z = $130,000.
25.
a) Optimal solution at B: x1 = 333.3 and x2 = 166.7
(333.3) + (166.7) − s1 = 400
s1 = 100 extra gallons of
blended whiskey produced
.6(333.33) − .4(166.7) − s2 = 0
s2 = 133.3 extra gallons
of rye in the blend
(166.7) + s3 = 250
s3 = 83.3 fewer gallons of bourbon
than the maximum
(333.3) + (166.7) + s4 = 500
s4 = 100 gallons of blend
production capacity left over
b) Because the “solution space” is not really an
area, but a line instead, the objective function
coefficients can change to any positive value
and the solution point will remain the same,
i.e., point B. Observing the graph of this
model, no matter how flatter or steeper the
objective function becomes, point B will
remain optimal.
26. Z = 1,666.667 (Wait until I complete Computer-based Sensitivity Analysis)
Variable Value
x1 333.333
x2 166.667
Constraint
Slack/Surplus
Shadow
Price
c1 100.000 0.000
c2 133.333 0.000
c3 83.333 0.000
c5 0.000 3.333
Objective Coefficient ranges
Variables
Lower
Limit
Current
Values
Upper
Limit
Allowable
Increase
Allowable
Decrease
x1 −2.000 3.000 No limit No limit 5.000
x2 −6.000 4.000 No limit No limit 10.000
Right hand side ranges
Constraints
Lower Limit Current
Values
Upper
Limit
Allowable
Increase
Allowable
Decrease
c1 No limit 400.000 500.000 100.000 No limit
c2 No limit 0.000 133.333 133.333 No limit
c3 166.667 250.000 No limit No limit 83.333
c4 −250.000 0.000 500.000 500.000 250.000
c5 400.000 500.000 750.000 250.000 100.000
Z = 1,625.000
Variable Value
x1 375.000
x2 125.000
Constraint Slack/Surplus Shadow Price
c1 100.000 0.000
c2 175.000 0.000
c3 125.000 0.000
c5 0.000 3.250
Objective Coefficient ranges
Variables Lower Limit Current Values Upper Limit Allowable Increase Allowable Decrease
x1 −1.333 3.000 No limit No limit 4.333
x2 −9.000 4.000 No limit No limit 13.000
Right hand side ranges
Constraints Lower Limit Current Values Upper Limit Allowable Increase Allowable Decrease
c1 No limit 400.000 500.000 100.000 No limit
c2 No limit 0.000 175.000 175.000 No limit
c3 125.000 250.000 No limit No limit 125.000
c4 −500.000 0.000 500.000 500.000 500.000
c5 400.000 500.000 1,000.000 500.000 100.000
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