college math assignment help
Question 1
1. 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
Answer
True
False
Question 2
1. Product mix problems cannot have “greater than or equal to” (≥) constraints.
Answer
True
False
Question 3
1. In a balanced transportation model, supply equals demand such that all constraints can be treated as equalities.
Answer
True
False
Question 4
1. In formulating a typical diet problem using a linear programming model, we would expect most of the constraints to be related to calories.
Answer
True
False
Question 5
1. A systematic approach to model formulation is to first construct the objective function before determining the decision variables.
Answer
True
False
2 points
Question 6
1. When using a linear programming model to solve the “diet” problem, the objective is generally to maximize profit.
Answer
True
False
Question 7
1. The following types of constraints are ones that might be found in linear programming formulations:
1.
≤
2.
=
3.
>
Answer
1 and 2
2 and 3
1 and 3
all of the above
2 points
Question 8
1. 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 9
1. 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:
Answer
.5A + .75B = 20
.3B = 20
.3 B≤ 20
.3B ≥ 20
2 points
Question 10
1. 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
2 points
Question 11
1. 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
2 points
Question 12
1. 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.
Answer
x21 + x22 ≤ 8000
x12 + x22 ≥ 8000
x11 + x12 ≤ 8000
x21 + x22 ≥ 8000
2 points
Question 13
1. Balanced transportation problems have the following type of constraints:
Answer
≥
≤
=
all the above
Question 14
1. 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 15
1. 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
Answer
MAX .06X1 +.08X2 +.11X3
MAX .06(15)X1 +.08(47.25)X2 +.11(110)X3
MAX 15X1 + 47.25X2 +.110X3
MAX (1/.06)X1 +.(1/08)X2 + (1/.11)X3
2 points
Question 16
1. If Xij = the production of product i in period j, write an expression to indicate that the limit on production of the company’s 3 products in period 2 is equal to 400.
Answer
X21 + X22 + X23 ≥ 400
X21 + X22 + X23 ≤ 400
X12 + X22 + X32 ≥ 400
X12 + X22 + X32 ≤ 400
2 points
Question 17
1. A croissant shop produces 2 products: bear claws (B) and almond filled croissants (C). Each bear claw requires 6 ounces of flour, 1 ounce of yeast, and 2 TS of almond paste. An almond filled croissant requires 3 ounces of flour, 1 ounce of yeast, and 4 TS of almond paste. The company has 6600 ounces of flour, 1400 ounces of yeast, and 4800 TS of almond paste available for today’s production run. Bear claw profits are 20 cents each, and almond filled croissant profits are 30 cents each. What is the optimal daily profit?
Answer
$380
$400
$420
$440
2 points
Question 18
1. 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 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
2 points
Question 19
1. 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?
Answer: .9x + .3y ≤ 10,000
Question 20
1.
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 oil based paint should the Quickbrush make?
Ans: 9167 gallons of water based paint and 5833 gallons of oil based paint
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