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candidate wants to use a combination of radio and television advertisements in her campaign. Research has shown that each 1-minute spot on television reaches 0.09 million people and that each 1-minute spot on radio reaches 0.006 million. The candidate believes she must reach at least 2.16 million people, and she must buy a total of at least 80 minutes of advertisements. How many minutes of each medium should be used to minimize costs if television costs $900/minute and radio costs $200/minute?

Respuesta :

adioabiola

The number of minutes of each medium should be used to minimize costs if television costs $900/minute and radio costs $200/minute is 45 minutes and 3.33 minutes respectively.

Inequality

  • Number of minutes of television advertising = x
  • Number of minutes of radio advertising = y

x ≥ 0

y ≥ 0

x + y ≤ 80

0.09x + 0.006y ≤ 2.16

From (1)

x ≤ 80 - y

  • Substitute into (2)

0.09x + 0.006y ≤ 2.16

0.09(80 - y) + 0.006y ≤ 2.16

7.2 - 0.09y + 0.006y ≤ 2.16

7.2 - 0.084y ≤ 2.16

-0.084y ≤ 2.16 - 7.2

-0.084y ≤ -5.04

y ≤ -5.04 / -0.084

y ≤ 60

  • Substitute into (1)

x + y ≤ 80

x + 60 ≤ 80

x ≤ 80 - 60

x ≤ 20

The number of minutes of each medium should be used to minimize costs if television costs $900/minute and radio costs $200/minute is

Television = $900 / 20

= 45 minutes

Radio = $200/60

= 3.33 minutes

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