Math451 Alternate Optimal Solutions Questions
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School
Colorado Technical University *
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Course
451
Subject
Mathematics
Date
Jan 9, 2024
Type
docx
Pages
5
Uploaded by JudgeKnowledgeCheetah31
Math451 Alternate Optimal Solutionsin
Questions
Question 1
suppose of the following constraints are redundant?
You are in the business of baking bread and cake. A loaf of bread is sold for $2 and a cake for $3. Bread takes 5 minutes and cake takes 4 minutes to bake. Bread takes 0.15 pound of flower dough and cake takes 0.6 pound. You have 6 2/3 hours of labor and 43.2 pounds of flower dough.
x ≥ 0
y ≥ 0
5x + 7.5y ≤ 400
Weight constraint
Solution
The correct answer is:
Weight constraint
Correct
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Question 2
When drawing pictures, think of regions where the objective function has the same value as a set of parallel lines and where the objective function takes a different value on each of the different lines. Suppose you wanted to plot a perpendicular line through these. Assuming that the parallel lines all have slope m, what can be said about the slope M of the perpendicular line?
m + M = (-1)
m + M = 0
m × M = (-1)
m + M = 1
Solution
The correct answer is:
m × M = (-1)
Correct
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Question 3
It is easier to visualize what is going on in two dimensions. The following figure shows a simplified feasible region:
Look at the slanted line , which represents the limit of one of the constraints and runs between the corners B and C. For specificity let point
and let
. Which of the following objective functions will allow for any point along
, including the points B and C, to be optimal?
Solution
The correct answer is:
Correct
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Question 4
It is easier to visualize what is going on in two dimensions. The following figure shows a simplified feasible region:
Look at the slanted line
, which represents the limit of one of the constraints and runs between the corners B and C. For specificity let point
and let
. Suppose that the objective function is maximized on the segment
and that a solution in whole numbers is required.
Suppose B = (10, 35.5) and C = (44, 15.35). How many solutions in integers can you find?
One
Four
Three
Zero
Solution
The correct answer is:
Zero
Correct
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Question 5
What is the value of the objective function maximizing the revenue?
You are in the business of baking bread and cake. A loaf of bread is sold for $2 and a cake for $3. Bread takes 5 minutes and cake takes 4 minutes to bake. Bread takes 0.4 pound of flower dough and cake takes 0.6 pound. You have 6 2/3 hours of labor and 43.2 pounds of flower dough.
$216
$0
$300
$160
Solution
The default answer is:
$216
Wrong
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Question 6
What is the value of the objective function maximizing the revenue?
You are in the business of baking bread and cake. A loaf of bread is sold for $2 and a cake for $3. Bread takes 5 minutes and cake takes 4 minutes to prepare. One loaf of bread uses 0.15 pounds of flour and one cake uses 0.6 pounds. You have 6 2/3 hours of labor and 43.2 pounds of flour.
$300
$160
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$251
$216
Solution
The correct answer is:
$251
Wrong
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Question 8
Suppose that two points, a and b, in the feasible region have the same value of the objective function, r. What can be said about the value of the objective function at any point on the line connecting a and b?
All the points are in the feasible region.
The value of the objective function can be no more than r
2
.
It is possible that part of the line will lie outside the feasible region.
It can take on any value between -r and r.
Solution
The correct answer is:
All the points are in the feasible region.
Correct
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Question 2
It is easier to visualize what is going on in two dimensions. The following figure shows a simplified feasible region:
Look at the horizontal line
, which represents the limit of one of the constraints and runs between the corners. For specificity, let point
and let
. What constraint does these points represent?
Solution
The correct answer is:
Wrong
Hide solution