MATHEMATICS

Question 10

 

 

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?

Answer

 

2R + 4D ≤ 480

 

2D + 4R ≤ 480

 

2R + 3D ≤ 480

 

3R + 2D ≤ 480

 

 

Question 11

 

 

The owner of Chips etc. produces 2 kinds of chips: Lime (L) and Vinegar (V). He has a limited amount of the 3 ingredients used to produce these chips available for his next production run: 4800 ounces of salt, 9600 ounces of flour, and 2000 ounces of herbs. A bag of Lime chips requires 2 ounces of salt, 6 ounces of flour, and 1 ounce of herbs to produce; while a bag of Vinegar chips requires 3 ounces of salt, 8 ounces of flour, and 2 ounces of herbs. Profits for a bag of Lime chips are $0.40, and for a bag of Vinegar chips $0.50.

What is the constraint for salt?

Answer

 

6L + 8V ≤ 4800

 

1L + 2V ≤ 4800

 

3L + 2V ≤ 4800

 

2L + 3V ≤ 4800

 

 

 

Question 12

 

 

When systematically formulating a linear program, the first step is

Answer

 

Construct the objective function

 

Formulate the constraints

 

Identify the decision variables

 

Identify the parameter values

 

 

 

Question 13

 

 

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?

Answer

 

x 1B + x 2B +x 3B = 600

 

x B1 + x B2 +x B3 = 150

 

x 1B + x 2B +x 3B = 150

 

none of the above

 

 

 

Question 14

 

 

Balanced transportation problems have the following type of constraints:

Answer

 

 

 

=

 

all the above

 

 

Question 15

 

 

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

Answer

 

X2 ≤ 10000

X2 + X3 ≤350

 

10,000 X2 ≤ 350X2 + 350X3

 

47.25X2 ≤10,000

X2 + X3 ≤ 350

 

47.25X2 ≤10,000

47.25 X2 + 110X3 ≤ 350

 

 

Question 16

 

 

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

Answer

 

They maximize profit.

 

The constraints are all equality constraints with no “≤” or “≥” constraints.

 

They contain fewer variables.

 

The solution values are always integers.

 

 

 

Question 17

 

 

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 constraint production time (8 hours = 480 minutes per day) and syrup (1 of her ingredient) 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 optimal daily profit?

 

Answer

 

$220

 

$420

 

$320

 

$280

 

 

 

Question 18

 

 

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:

Answer

 

.4×2 – .6×7 – .6×8 ≤ 0

 

x2 ≥ .60 (x2 + x7 + x8)

 

.4×2 – .6×7 – .6×8 ≥ 0

 

-.4×2 + .6×7 + .6×8 ≤ 0

 

 

 

Question 19

 

 

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

 

Answer

 

 

 

Question 20

 

 

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.

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