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Maximum value of z = 21

Minimum value of z = -9

Step-by-step explanation:

We have to maximize/minimize the given equation for the given constraints as,

x ≥ -1

y ≤ -2x + 3

y ≥ -1

By using the graphing tool,

Corner points for the feasible region are,

A(-1, 5), B(-1, -1) and C(2, -1)

For A(-1, 5),

z = 4x + 5y = 4(-1) + 5(5)

                  = -4 + 25

                  = 21

For B(-1, -1),

z = 4(-1) + 5(-1)

  = -4 - 5

  = -9

For C(2, -1),

z = 4(2) + 5(-1)

  = 8 - 5

  = 3

Maximum value of z = 21

Minimum value of z = -9

answer is 8x+24

area of vanessa's patio = length × width

given, length = (3x² + 5x + 10)

width = (x² - 3x - 1)

area of vanessa's patio = (3x² + 5x + 10)(x² - 3x - 1)

= 3x²(x² - 3x - 1) + 5x(x² - 3x - 1) + 10(x² - 3x - 1)

= 3x⁴ - 9x³ - 3x² + 5x³ - 15x² - 5x + 10x² - 30x - 10

= 3x⁴ - 4x³ - 8x² - 35x - 10

hence, expression of vanessa's patio = (3x⁴ - 4x³ - 8x² - 35x - 10)

you first to choose the points and then move from then as the slope you have