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I'm looking for some help with these questions. The answer that best helps and answers the question will receive brainliest. This is also worth 100 points.
Thank you very much for your help!

1.
A feasible region is bounded by the constraints:
{ [tex]y\leq 20-x[/tex]
{ [tex]y\geq 20-4x[/tex]
{ [tex]y\geq 5-0.25x[/tex]

The objective function is P = 3x + 5y
(a) Graph the feasible region.
(b) Find the value of the objective function at each vertex of the feasible region.
(c) What is the minimum value of the objective function, P?
(d) At which point does the minimum value occur?
Show all work.

2.
In 2010, the population of a town was 8500. The population decreased by 4.5% each year.
(a) Write an equation to find the population of the town t years after 2010.
(b) In what year will the population be 7000?
Show your work.

Respuesta :

mhanifa

Step-by-step explanation:

Question 1

(a)

  • See the attached graph

(b)

The vertices are:

  • (0, 20), (20, 0) and (4, 4)

The objective function:

  • P = 3x + 5y

Find the value of P at each vertex:

  • P = 3*0 + 5*20 = 100
  • P = 3*20 + 5*0 = 60
  • P = 3*4 + 5*4 = 32

(c) and (d)

  • The minimum value of P is 32 at vertex (4, 4)

Question 2

Given:

  • Initial population = 8500
  • Decrease rate = 4.5% or 0.045

(a)

Required equation:

  • y = 8500*(1 - 0.045)ˣ = 8500*(0.955)ˣ, where x- is the number of years after 2010

(b)

If y = 7000, find the value of x:

  • 7000 = 8500*(0.955)ˣ
  • (0.955)ˣ = 7000/8500
  • (0.955)ˣ = 0.8235
  • log (0.955)ˣ = log 0.8235
  • x  =  log 0.8235/ log 0955
  • x = 4.21 (rounded)

2010 + 4.21 years ⇒ in the year 2015

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