Agraph represents the feasible region for the system: y is less than or equal to 2x, x + y is greater than or equal to 45, and x is less than or equal to 30. what is the minimal number for the objective function p = 20x + 16y? what is the value of x then? what is the value at y then?

We are given a system of inequalities as:

y is less than or equal to 2x

i.e.          y ≤ 2x--------(1)

x + y is greater than or equal to 45

i.e.      x+y ≥ 45  ------------(2)    

and    x is less than or equal to 30.    

i.e.               x ≤ 30 -----------(3)    

On plotting these inequalities we get the boundary points as:

         (15,30) , (30,60) and (30,15)    

( Since, the optimal solution always exist at the boundary point )

The optimal function is given by:

 Minimize  P = 20x+16y

Hence, at (15,30) we get:

P= 780

at (30,60) we get:

  P= 1560

at (30,15) we get:

P= 840

This  means that the minimal value of the function is 780

and the value exist at (15,30)

30 units^2

step-by-step explanation:

area is l × w

the length is 3

and the width is 10

3 × 10= 30 units squared

let's call the solutions x₁ = (5 - 2√7)/3 and x₂ = (5 + 2√7)/3

then the equation is (x-x₁)(x-x₂) = 0

if you fill that in you get a lot of numbers which you can recognize as ax²+bx+c=0.

step-by-step explanation:

you can see that a=1 (there is just an x²)

b = (-5 -2√7 + 2√7 - 5)/3 = -10/3

c = -2√7)/3 ) * (-5+2√7)/3) = -1/3

so your answer is 3x^2 – 10x – 1 = 0