MAT 540 WEEK 7 QUIZ 3 Week Quiz
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

$15.00ANSWERTutor has posted answer for $15.00. See answer's preview
******** **
In * ****** *********** ******* *** model ********** are ******* ** ** known **** **********
*******
*****
******
******** **
********* ********* ** linear programming ******** have ** ******** ****** ** ******** objective ******** ******
*******
*****
******
******** **
In ************ ** ******** *** ******** region ** ****** below *** ******** ************
Answer
*****
******
******** **
Surplus ********* *** **** ********** with ************ problems
*******
*****
******
Question 5
** *** ********* ******** ** parallel ** * constraint the ********** ** ***********
*******
*****
******
Question **
* ****** programming ***** ******** of only ******** ********* *** ************
*******
*****
******
Question **
* ******** ******** ******** at ***** *** of *** ************
Answer
True
******
******** 8
*** ********* ** a graph of * ****** *********** ******* *** ******** ******** space is shaded *** *** ******* ******** ** ** *** ***** labeledZ*
(graph did not copy/paste)
***** of *** ********* *********** *** * ******* greater than 0?
*******
***
***
***
AJ
******** 9
***** ********* buys * products *** ******* *** ******* *** *** medium shelves *** **** *** ***** ***** **** *** ******** *** cubic **** ** ******* ***** *** each ****** ***** costs **** *** requires 90 ***** feet ** ******* ***** *** ******* *** ****** to ****** in ******* **** **** *** the warehouse *** 18000 ***** **** ********* for ******* ****** *** **** *** ***** ** **** *** for each ****** ***** ** $150 What ** *** ******* ********
*******
*******
*******
*******
*******
*******
******** ***
*** following ** * ***** ** * linear *********** ******* *** ******** ******** space is ****** *** *** ******* ******** ** ** *** point labeledZ*
***** did not copy/paste
*** ******** for ********** ** ****
Answer
** * ** **** ***
8X * 4Y ≥ 32
* * 2Y **** 8
** * * ≥ **
******** 11
*** ********** ******* for *** ***** **** drink ******* ** considering *** ********** ** 2 ***** ** **** ******* regular *** **** *** ** her limited ********* *** production **** ** ***** * *** ******* *** day) *** ***** ** of *** ************ ******* ** *** gallons *** *** To produce * ******* **** requires 2 ******* *** 5 ******* of ***** ***** * diet **** ***** * ******* *** 3 ******* ** ***** ******* for ******* soft ***** *** **** *** **** *** profits *** diet soft drink *** $200 *** case For *** production *********** ** *** ***** ** regular and ***** of **** **** drink ***** ********* **** not ** ********** ******
Answer
**** *****
**** syrup
time and ******
neither **** nor ******
Question ***
In a ****** *********** ******* *** ******* constraints for *** ******* ******** *****
*** * *** ≤ ***
2x1 * 5x2 **** ***
***** ** ***** objective ********* will **** ** *** same ******* **********
Answer
*** + 1x2
7x1 * 8x2
**** * *****
**** * 15x2
******** ***
In * linear *********** problem * valid objective function can ** *********** ***
Answer
*** * * 5xy
*** * *** * ****
*** ** * ** * *****
*** *** * x2) * ***
******** ***
***** furniture **** * products for resale: big ******* (B) *** medium shelves (M) **** *** ***** ***** **** *** ******** *** cubic feet of ******* ***** *** **** medium ***** ***** $300 *** ******** ** cubic **** of ******* ***** *** ******* *** $75000 ** invest in ******* this **** *** the ********* *** ***** ***** **** ********* for ******* ****** *** **** *** ***** ** $300 *** *** each ****** ***** ** $150 What is *** objective **********
*******
*** Z * ***** + $100 **
*** Z * $300M * $150 **
*** * * ***** * **** M
*** Z = ***** * **** **
Question 15
A graphical ************** of * ****** ******* ** shown ***** The shaded **** ********** *** ******** region *** the ****** line ** *** middle ** the ***** ** *** ********* function
***** *** not copy/paste
If **** is * ************ ***** ******* ***** ** *** ******* **********
*******
***** B
***** **
***** **
***** **
******** ***
*** following ** a graph ** * linear *********** ******* *** ******** ******** space ** ****** and *** ******* ******** ** at *** point **********
***** *** *** ***********
**** ****** *********** problem is a:
Answer
************ problem
************ ********
********* ********
cannot **** **** *** *********** ******
Question 17
*** ********** ******* *** *** ***** **** ***** ******* ** *********** *** production ** * ***** ** **** ******* ******* *** and ******* *** ** the limited ********* *** production **** (8 ***** = 480 ******* *** **** *** ***** ******* to *** gallons per *** ** produce * ******* **** ******** * minutes *** 5 ******* of ***** ***** * **** case ***** * minutes and 3 ******* ** syrup ******* *** ******* **** drink *** **** per **** and ******* *** diet soft ***** *** **** *** **** **** is *** time ************
*******
2R * ** **** ****
** * ** **** ****
** * 3D ≤ 480
** * 4D **** ****
Question ***
***** *** ********* ************
*** * * *** +4x2
** ** * 2x2 ≤ ***
*** * 3x2 ≤ 18
** **** **
** ≤ ***
** ** **** ****
the optimal ******** **** is *** value ** *** ********* ******** ** the optimal ********* Note: *** ****** will ** ** integer Please give **** ****** ** ** ******* ******* *** ******* ***** *** example *** ******* ***** ***** be ******* *** *******
Question
*** ***
* * $3x + **** *******
*** 20x * *** **** ***** 4x
* 2y **** 240 *
**** *** x
y ≥ ** the
optimal solution **** is *** amount of slack ********** **** *** ****** ************ ******* ********
20
******** ***
********* ****** *********** ********* *** *
* **** * ***** ******* ***
** + 5y **** 40 04x +
y **** ** x *
**** At the *******
solution **** ** *** ****** ** slack ********** **** the first ************ ******
Click here to download attached files:MAT 540 WEEK 7 QUIZ 3.docx