Chapter:–
Student:|frrF 1.
Graph the linear inequality.
x*zy> – 4
tnstructorlf Course:I Assignment: Chapter 3
2.
Use the graphing toolto graph the inequality.
Graph the feasible region for the following system of inequalities. Tell whether the region is bounded or unbounded.
x+4y<16 4x+ 5y >20
Use the graphing tool on the right to graph the system of inequalities.
ls the region bounded or unbounded?
unbounded
bounded
Graph the feasible region for the system of inequalities. Tell whether the region is bounded or unbounded.
– 1 <x<2 -1<ys3 zx+y<S
Use the graphing toolto graph the system.
The region is (1)
bounded.
unbounded.
3.
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(1)
e
4. A dietician is planning a snack package of fruit and nuts. Each ounce of fruit will supply 1 unit of protein, 2 units of
carbohydrates, and 1 unit of fat. Each ounce of nuts will supply 1 unit of protein, 1 unit of carbohydrates, and 1 unit
of fat. Every package must provide at least 7 units of protein, at least 12 units of carbohydrates, and no more than
10 units of fat. Let x equal the ounces of fruit and y equal the ounces of nuts to be used in each package.
a. Write a system of inequalities to express the conditions of the problem.
b. Graph the feasible region of the system.
a. Fill in the chart.
Let x be the number of ounces of fruit and y the number of ounces of nuts. Referring to the chart, give the three inequalities that x and y must satisfy because of the package’s requirements for protein, fat, and carbohydrate.
>7
>12
<10
Give the inequalities that x and y must satisfy because they cannot be negative.
y>
x>
b. Graph the feasible set for the packaging problem. The feasible set is shaded.
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5. The graph to the right shows a region of feasible solutions. Use this region to find maximum and minimum values of the given objective functions, and the locations of these values on the graph.
(alz=6x+3y (blz=x+9y
(a) What is the maximum of z = 6x + 3y? Select the correct answer below and, if necessary, fill in the answer boxes to complete your choice.
i”- i A. The maximum value of the objective function z = (
gvp;;;i;;i ;:::”:i”cated at the point
i_”: B. The maximum does not exist.
What is the minimum of z = 6x + 3y? Select the correct answer below and, if necessary, fill in the answer boxes to complete your choice.
t A. The minimum value of the objective function z = 6 and is located at the point
(Type an exact answer.)
t*: B. The minimum does not exist.
(b) What is the maximum of z = x + 9y? Select the correct answer below and, if necessary, fill in the answer boxes to complete your choice.
{“-.j A. The maximum value of the objective function z = > and is located at (Type an exact answer.)
i.-.i g. fne maximum does not exist.
What is the minimum of z- x + 9y? Select the correct answer below and, if necessary fill in the answer boxes to complete your choice.
i*.i A. me minimum value of the objective function z = x and is located (Type an exact answer.)
,-“t g. The minimum does not exist.
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b. Solve the following linear programming problem.
Maximize: z=7x+3y subject to: 4x’y <14
2y+y>13 x>3 ys9
The maximum value is
(Type an integer or. ”
titnptif’eO trr.tion)
The maximum occurs at the point
(Type an ordered pair. Type an integer or a simplified fraction.)
7. Write the constraint below as a linear inequality.
A canoe requires 3 hours of fabrication and a rowboat 7 hours. The fabrication department has at most 86 hours of labor available each week. Let x be the number of canoes and let y be the number of rowboats.
Choose the inequality that represents the given constraint.
A. 7x+3ys86 B. 3x+7y<86 C. 3x+7y>86 D. 7x+3y>86
8. A dairy company gets milk from two dairies and then blends the milk to get the desired amount of butterfat. Milk from dairy I costs $2.40 per gallon, and milk from dairy ll costs $0.80 per gallon. At most $144 is available for purchasing milk. Dairy I can supply at most 50 gallons averaging 3.7% butterfat, and dairy ll can supply at most
80 gallons averaging 2.9% butterfat. Answer parts a and b.
a. How much milk from each supplier should the company buy to get at most 100 gallons of milk with the maximum
amount of butterfat?
The company should buy gallons from dairy I and gallons from dairy ll.
What is the maximum amount of butterfat?
gallons
(Type an integer or a decimal.)
b. The solution from part a leaves both dairy I and dairy ll with excess capacity. Calculate the amount of additional
milk each dairy could produce.
The excess capacity of dairy I is gallons, and for dairy ll it is gallons.
ts there any way all this capacity could be used while still meeting the other constraints? Explain.
:.- t A. No. Any more milk purchased from either dairy will go over budget. r.. r B. Yes, 10 more gallons can be bought from dairy I and 20 more from dairy ll without going over budget. i”r C. Yes, 10 more gallons can be bought from dairy I without going over budget- i .: D. Yes, 10 more gallons can be bought from dairy I without going over budget.
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9. A patient takes vitamin pills. Each day he must have at least 600 lU of vitamin A, I mg of vitamin B1 , and 25 mg of vitamin C. He can choose between pill 1 , which contains 420 lU of vitamin A, 2 mg of vitamin B, , and 5 mg of
vitamin C, and pill 2, which contains 60 lU of vitamin A, 2 mg of vitamin B., , and 10 mg of vitamin C. Pill 1 costs
309, and pill2 costs 15P. Complete parts a and b below
a. How many of each pill should he buy in order to minimize his cost? What is the minimum cost?
He should buy of pill 1 and of pill 2. The minimum cost is $ (Simplify your answers. Type integers or decimals.)
b. For the solution in part a, the patient is receiving more than he needs of at least one vitamin. ldentifiT that
vitamin, and tell how much surplus he is receiving.
He is receiving lU of vitamin A, mg of vitamin B1 , and mg of
vitamin C more than he needs. (Simplify your answers.)
ls there any way he can avoid receiving that surplus while still meeting the other constraints and minimizing cost? Explain. Choose the correct answer below.
t _,: A. Yes. Take one fewer of each pill to reduce the cost. i.,., B. No. Reducing the surplus would either cause the cost to increase or cause the patient to receive less
than needed of anoiher vitamin.
L _-, G. Yes. Reverse the numbers of each pitl taken.
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