Question

Find the value of the revenue function R at each vertex.

a. Value of R at vertex 1.
b. Value of R at vertex 2.
c. Value of R at vertex 3.
d. Value of R at vertex 4.

Coordinates of Vertex's:
Vertex 1 - (0,0)
Vertex 2 - (60,60)
Vertex 3 - (90,40)
Vertex 4 - (100,0)

Answer 1

The revenue function is given by a quadratic equation. The value of R at each vertex can be calculated by substituting the x-coordinate of the vertex into the revenue function equation.

The revenue function is given by the quadratic equation
`R(x) = ax^2 + bx + c` , where a = 1.00, b = 10.0, and c = -200.

a. Value of R at vertex 1:

At vertex 1, x = 0. Substitute x into the revenue function equation:

R(0) = 1.00
`(0)^2` + 10.0(0) - 200 = -200

Therefore, the value of R at vertex 1 is -200.

b. Value of R at vertex 2:

At vertex 2, x = 60. Substitute x into the revenue function equation:

R(60) = 1.00
`(60)^2` + 10.0(60) - 200 = 3600 + 600 - 200 = 4000

Therefore, the value of R at vertex 2 is 4000.

c. Value of R at vertex 3:

At vertex 3, x = 90. Substitute x into the revenue function equation:

R(90) = 1.00
`(90)^2` + 10.0(90) - 200 = 8100 + 900 - 200 = 8800

Therefore, the value of R at vertex 3 is 8800.

d. Value of R at vertex 4:

At vertex 4, x = 100. Substitute x into the revenue function equation:

R(100) = 1.00
`(100)^2` + 10.0(100) - 200 = 10000 + 1000 - 200 = 10800

Therefore, the value of R at vertex 4 is 10800.