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

The minimum value is 24.

Given Information:

The system of inequality is,

Objective function:f=5x+2yConstraints:2x+y≥124x+3y≥30x+2y≥10x≥0,y≥0

Calculation:

Consider the given system of inequality,

Objective function:f=5x+2yConstraints:2x+y≥124x+3y≥30x+2y≥10x≥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.

2x+y=124x+3y=30x+2y=10

Find the intersecting points between the equations.

Substitute x=10−2y in the second equation.

410−2y+3y=3040−8y+3y=3010=5yy=2

The obtained point is 6,2 .

Substitute y=12−2x in the second equation.

4x+312−2x=304x+36−6x=306=2xx=3

The obtained point is 3,6 .

Substitute x=0 in the first equation.

20+y=12y=12

The obtained point is 0,12 .

Substitute y=0 in the third equation.

x+20=10x=10

The obtained point is 10,0 .

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 12 for y in the objective function.

f=50+212=24

Substitute 3 for x and 6 for y in the objective function.

f=53+26=27

Substitute 6 for x and 2 for y in the objective function.

f=56+22=34

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

f=510+20=50

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 24.

Chapter 7.4, Problem 34E

Chapter 7.4, Problem 36E

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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