MAT540 Quiz 4 - A Graded Solution - 41131

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·         Question 1 

 

 

 

Product mix problems cannot have "greater than or equal to" (≥) constraints. 

 

 

 

 

 

 

 

·         Question 2

 

 

When using a linear programming model to solve the "diet" problem, the objective is generally to maximize profit. 

 

 

 

 

 

 

 

·         Question 3 

 

 

 

In formulating a typical diet problem using a linear programming model, we would expect most of the constraints to be related to calories. 

 

 

 

 

 

 

 

·         Question 4 

 

 

 

The standard form for the computer solution of a linear programming problem requires all variables to be to the right and all numerical values to be to the left of the inequality or equality sign?

 

 

 

 

 

 

 

·         Question 5

 

 

 

Fractional relationships between variables are permitted in the standard form of a linear program.

 

 

 


 

 

 

 

·         Question 6 

 

 

 

In a transportation problem, a demand constraint (the amount of product demanded at a given destination) is a less-than-or equal-to constraint (≤). 

 

 

 


 

 

 

 

·         Question 7 

 

 

 

The owner of Black Angus Ranch is trying to determine the correct mix of two types of beef feed, A and B which cost 50 cents and 75 cents per pound, respectively.  Five essential ingredients are contained in the feed, shown in the table below.  The table also shows the minimum daily requirements of each ingredient.

Ingredient

Percent per pound in Feed A

Percent per pound in Feed B

Minimum daily requirement (pounds)

1

20

24

30

2

30

10

50

3

0

30

20

4

24

15

60

5

10

20

40


 
The constraint for ingredient 3 is:

 

 

 

 

 

 

 

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·         Question 15

 

 

 

Let xij = gallons of component i used in gasoline j. Assume that we have two components and two types of gasoline. There are 8,000 gallons of component 1 available, and the demand gasoline types 1 and 2 are 11,000 and 14,000 gallons respectively. Write the supply constraint for component 1.

 

 

 

 

 

 

 

·         Question 16 

 

 

 

The production manager for the Softy soft drink company is considering the production of 2 kinds of soft drinks: regular and diet. Two of her resources are production time (8 hours = 480 minutes per day) and syrup (1 of the 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. What is the time constraint?

 

 

 


 

 

 

 

·         Question 17 

 

 

 

Assume that x2, x7 and x8 are the dollars invested in three different common stocks from New York stock exchange. In order to diversify the investments, the investing company requires that no more than 60% of the dollars invested can be in "stock two". The constraint for this requirement can be written as:

 

 

 

       
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