Mat 540 week 7 quiz 3 week quiz question 1 in a linear programming

Question 1

In a linear programming problem, all model parameters are assumed to be known with certainty.

Answer
True
False
Question 2
Graphical solutions to linear programming problems have an infinite number of possible objective function lines.
Answer
True
False
Question 3
In minimization LP problems the feasible region is always below the resource constraints.
Answer
True
False
Question 4
Surplus variables are only associated with minimization problems.
Answer
True
False
Question 5
If the objective function is parallel to a constraint, the constraint is infeasible.
Answer
True
False
Question 6
A linear programming model consists of only decision variables and constraints.
Answer
True
False
Question 7
A feasible solution violates at least one of the constraints.
Answer
True
False
Question 8
The following is a graph of a linear programming problem. The feasible solution space is shaded, and the optimal solution is at the point labeledZ*.
(graph did not copy/paste)
Which of the following constraints has a surplus greater than 0?
Answer
BF
CG
DH
AJ
Question 9
Cully furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is $300 and for each medium shelf is $150. What is the maximum profit?
Answer
$25000
$35000
$45000
$55000
$65000
Question 10
The following is a graph of a linear programming problem. The feasible solution space is shaded, and the optimal solution is at the point labeledZ*.
graph did not copy/paste
The equation for constraint DH is:
Answer
4X + 8Y ≥ 32
8X + 4Y ≥ 32
X + 2Y ≥ 8
2X + Y ≥ 8
Question 11
The production manager for the Coory soft drink company is considering the production of 2 kinds of soft drinks: regular and diet. Two of her limited resources are production time (8 hours = 480 minutes per day) and syrup (1 of her ingredients) limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. For the production combination of 135 cases of regular and 0 cases of diet soft drink, which resources will not be completely used?
Answer
only time
only syrup
time and syrup
neither time nor syrup
Question 12
In a linear programming problem, the binding constraints for the optimal solution are:
5×1 + 3×2 ≤ 30
2×1 + 5×2 ≤ 20
Which of these objective functions will lead to the same optimal solution?
Answer
2×1 + 1×2
7×1 + 8×2
80×1 + 60×2
25×1 + 15×2
Question 13
In a linear programming problem, a valid objective function can be represented as
Answer
Max Z = 5xy
Max Z 5×2 + 2y2
Max 3x + 3y + 1/3z
Min (x1 + x2) / x3
Question 14
Cully furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75000 to invest in shelves this week, and the warehouse has 18000 cubic feet available for storage. Profit for each big shelf is $300 and for each medium shelf is $150. What is the objective function?
Answer
MAX Z = $300B + $100 M
MAX Z = $300M + $150 B
MAX Z = $300B + $150 M
MAX Z = $300B + $500 M
Question 15
A graphical representation of a linear program is shown below. The shaded area represents the feasible region, and the dashed line in the middle is the slope of the objective function.
graph did not copy/paste
If this is a maximization, which extreme point is the optimal solution?
Answer
Point B
Point C
Point D
Point E
Question 16
The following is a graph of a linear programming problem. The feasible solution space is shaded, and the optimal solution is at the point labeledZ*.
graph did not copy/paste
This linear programming problem is a:
Answer
maximization problem
minimization problem
irregular problem
cannot tell from the information given
Question 17
The production manager for the Coory soft drink company is considering the production of 2 kinds of soft drinks: regular (R) and diet(D). Two of the limited resources are production time (8 hours = 480 minutes per day) and syrup limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3.00 per case and profits for diet soft drink are $2.00 per case. What is the time constraint?
Answer
2R + 5D ≤ 480
2D + 4R ≤ 480
2R + 3D ≤ 480
2R + 4D ≤ 480
Question 18
Solve the following graphically
Max z = 3×1 +4×2
s.t. x1 + 2×2 ≤ 16
2×1 + 3×2 ≤ 18
x1 ≥ 2
x2 ≤ 10
x1, x2 ≥ 0
Find the optimal solution. What is the value of the objective function at the optimal solution? Note: The answer will be an integer. Please give your answer as an integer without any decimal point. For example, 25.0 (twenty five) would be written 25
Answer

27
Question 19
Max Z = $3x + $9y
Subject to: 20x + 32y ≤ 1600
4x + 2y ≤ 240
y ≤ 40
x, y ≥ 0
At the optimal solution, what is the amount of slack associated with the second constraint?
Answer

96
Question 20
Consider the following linear programming problem:
Max Z = $15x + $20y
Subject to: 8x + 5y ≤ 40
0.4x + y ≥ 4
x, y ≥ 0
At the optimal solution, what is the amount of slack associated with the first constraint?
Answer

0

 

 

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