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Question 1


In a balanced transportation model, supply equals demand such that all constraints can be

treated as equalities.


Question 2


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



Question 3


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



Question 4


Product mix problems cannot have “greater than or equal to” (.) constraints.


Question 5


In formulating a typical diet problem using a linear programming model, we would expect most

of the constraints to be related to calories.


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


Balanced transportation problems have the following type of constraints:


Question 8


When systematically formulating a linear program, the first step is


Question 9


A systematic approach to model formulation is to first


Question 10


In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of stocks 1, 2,

an 3 which have selling prices of $15, $47.25, and $110, respectively. The investor stipulates

that stock 1 must not account for more than 35% of the number of shares purchased. Which

constraint is correct?


Question 11


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.


Percent per pound

in Feed A

Percent per pound

in Feed B

Minimum daily



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:


Question 12


In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of stocks 1, 2,

an 3 which have selling prices of $15, $47.25, and $110, respectively. The investor has up to

$50,000 to invest. The stockbroker suggests limiting the investments so that no more than

$10,000 is invested in stock 2 or the total number of shares of stocks 2 and 3 does not exceed

350, whichever is more restrictive. How would this be formulated as a linear programming



Question 13


The following types of constraints are ones that might be found in linear programming


1. .

2. =

3. >


Question 14


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 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


In a portfolio problem, X1, X2, and X3 represent the number of shares purchased of stocks 1, 2,

an 3 which have selling prices of $15, $47.25, and $110, respectively. The investor has up to

$50,000 to invest. The expected returns on investment of the three stocks are 6%, 8%, and

11%. An appropriate objective function is


Question 17


Small motors for garden equipment is produced at 4 manufacturing facilities and needs to be

shipped to 3 plants that produce different garden items (lawn mowers, rototillers, leaf

blowers). The company wants to minimize the cost of transporting items between the facilities,

taking into account the demand at the 3 different plants, and the supply at each manufacturing

site. The table below shows the cost to ship one unit between each manufacturing facility and

each plant, as well as the demand at each plant and the supply at each manufacturing facility.

What is the demand constraint for plant B?


Question 18


Compared to blending and product mix problems, transportation problems are unique because


Question 19


Quickbrush Paint Company makes a profit of $2 per gallon on its oil]base paint and $3 per

gallon on its water]base paint. Both paints contain two ingredients, A and B. The oil]base paint

contains 90 percent A and 10 percent B, whereas the water]base paint contains 30 percent A

and 70 percent B. Quickbrush currently has 10,000 gallons of ingredient A and 5,000 gallons of

ingredient B in inventory and cannot obtain more at this time. The company wishes to use

linear programming to determine the appropriate mix of oil]base and water]base paint to

produce to maximize its total profit. How many gallons of water based paint should the

Quickbrush make? Note: Please express your answer as a whole number, rounding the nearest

whole number, if appropriate.


Question 20


Kitty Kennels provides overnight lodging for a variety of pets. An attractive feature is the quality

of care the pets receive, including well balanced nutrition. The kennel’s cat food is made by

mixing two types of cat food to obtain the “nutritionally balanced cat diet.” The data for the

two cat foods are as follows:

Kitty Kennels wants to be sure that the cats receive at least 5 ounces of protein and at least 3

ounces of fat per day. What is the cost of this plan? Express your answer with two places to the

right of the decimal point. For instance, $9.32 (nine dollars and thirty]two cents) would be

written as 9.32

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