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Section 4.6 Text Problem # 9 Solution Manual ACS Page # 165 Solution Problem # 9. Chapter 4 Systems of Linear Equations. Section 4.6. Linear Programming. Chapter 4 Systems of Linear Equations. Section 4.6. Example #1.

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section 4 6

Chapter 4

Systems of Linear Equations

Section 4.6

Linear Programming

section 4 61

Chapter 4

Systems of Linear Equations

Section 4.6

Example #1

section 4 62

Chapter 4

Systems of Linear Equations

Section 4.6

Example #2

section 4 63

Chapter 4

Systems of Linear Equations

Section 4.6

Example #3

slide10

The publicity director for Mercy Hospital is planning to bolster the hospital’s image by running a TV ad and a radio ad. Due to budgetary and other constraints, the number of times she can run the TV ad, x, and the number of times that she can run the radio ad, y, must be in the region shown in the figure. The function:

A = 9000x + 4000y

gives the total number of people reached by the ads.

slide11

a)Find the total number of people reached by the ads at each vertex of the region.

b) What mix of TV and radio ads maximizes the number of people reached?

slide12

a)

Number of radio ads

Number of TV ads

A(0,0) =

0

320,000

A(0,80) = 9000(0) + 4000(80) =

A(50,0) = 9000(50) + 4000(0) =

450,000

A(30,60) = 9000(30) + 4000(60) =

510,000

slide13

Number of radio ads

Number of TV ads

b)

Maximum value at (30, 60).

To maximize the audience they should use 30 TV ads and 60 radio ads.