To calculate: The minimum and minimum value, checked they exists, of the objective function f .

The minimum value is 34.

Given Information:

The system of inequality is,

Objective function:f=3x+5yConstraints:3x+2y≥205x+6y≥522x+7y≥30x≥0,y≥0

Calculation:

Consider the given system of inequality,

Objective function:f=3x+5yConstraints:3x+2y≥205x+6y≥522x+7y≥30x≥0,y≥0

Use the graphing calculator to draw the inequality.

The polygonal region of feasible solutions has three vertices. To find these, solve each of the following system of boundary equations:

Write the inequality as equation and find the intersecting point.

3x+2y=205x+6y=522x+7y=30

Find the intersecting points between the equations.

Substitute x=0 in the first equation.

30+2y=202y=20y=10

The obtained point is 0,10 .

Substitute y=20−3x2 in the second equation.

5x+620−3x2=5210x+120−18x2=52120−104=8xx=2

The obtained point is 2,7 .

Substitute x=30−7y2 in the second equation.

530−7y2+6y=52150−35y+12y=10446=23yy=2

The obtained point is 8,2 .

Substitute y=0 in the third equation.

2x+70=302x=30x=15

The obtained point is 15,0 .

So, mentioned the point on the graph and shaded the common region.

Find the value of the objective function at the all vertices.

Substitute 0 for x and 10 for y in the objective function.

f=30+510=50

Substitute 2 for x and 7 for y in the objective function.

f=32+57=41

Substitute 8 for x and 2 for y in the objective function.

f=38+52=34

Substitute 15 for x and 0 for y in the objective function.

f=315+50=45

Since the feasible region is unbounded and has x≥0 and y≥0 , and conclude that there is no maximum value for the objective function.

Therefore, the minimum value is 34.

Chapter 7.4, Problem 35E

Chapter 7.4, Problem 37E

Chapter 7 Solutions

PRECALCULUS:GRAPHICAL,...-NASTA ED.

Ch. 7.1 - Prob. 1QR Ch. 7.1 - Prob. 2QR Ch. 7.1 - Prob. 3QR Ch. 7.1 - Prob. 4QR Ch. 7.1 - Prob. 5QR Ch. 7.1 - Prob. 6QR Ch. 7.1 - Prob. 7QR Ch. 7.1 - Prob. 8QR Ch. 7.1 - Prob. 9QR Ch. 7.1 - Prob. 10QR

Ch. 7.1 - Prob. 1E Ch. 7.1 - Prob. 2E Ch. 7.1 - Prob. 3E Ch. 7.1 - Prob. 4E Ch. 7.1 - Prob. 5E Ch. 7.1 - Prob. 6E Ch. 7.1 - Prob. 7E Ch. 7.1 - Prob. 8E Ch. 7.1 - Prob. 9E Ch. 7.1 - Prob. 10E Ch. 7.1 - Prob. 11E Ch. 7.1 - Prob. 12E Ch. 7.1 - Prob. 13E Ch. 7.1 - Prob. 14E Ch. 7.1 - Prob. 15E Ch. 7.1 - Prob. 16E Ch. 7.1 - Prob. 17E Ch. 7.1 - Prob. 18E Ch. 7.1 - Prob. 19E Ch. 7.1 - Prob. 20E Ch. 7.1 - Prob. 21E Ch. 7.1 - Prob. 22E Ch. 7.1 - Prob. 23E Ch. 7.1 - Prob. 24E Ch. 7.1 - Prob. 25E Ch. 7.1 - Prob. 26E Ch. 7.1 - Prob. 27E Ch. 7.1 - Prob. 28E Ch. 7.1 - Prob. 29E Ch. 7.1 - Prob. 30E Ch. 7.1 - Prob. 31E Ch. 7.1 - Prob. 32E Ch. 7.1 - Prob. 33E Ch. 7.1 - Prob. 34E Ch. 7.1 - Prob. 35E Ch. 7.1 - Prob. 36E Ch. 7.1 - Prob. 37E Ch. 7.1 - Prob. 38E Ch. 7.1 - Prob. 39E Ch. 7.1 - Prob. 40E Ch. 7.1 - Prob. 41E Ch. 7.1 - Prob. 42E Ch. 7.1 - Prob. 43E Ch. 7.1 - Prob. 44E Ch. 7.1 - Prob. 45E Ch. 7.1 - Prob. 46E Ch. 7.1 - Prob. 47E Ch. 7.1 - Prob. 48E Ch. 7.1 - Prob. 49E Ch. 7.1 - Prob. 50E Ch. 7.1 - 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