MAT540 Quantitative Methods Week 7 QUIZ 3 SOLUTION 20 20

Question: #1078

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:
5x1 + 3x2 ≤ 30
2x1 + 5x2 ≤ 20
Which of these objective functions will lead to the same optimal solution?
Answer
2x1 + 1x2
7x1 + 8x2
80x1 + 60x2
25x1 + 15x2
Question 13
In a linear programming problem, a valid objective function can be represented as
Answer
Max Z = 5xy
Max Z 5x2 + 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 = 3x1 +4x2
s.t. x1 + 2x2 ≤ 16
2x1 + 3x2 ≤ 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

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

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