A manufacturer has determined that the total cost C of operating a factory is C = 2.5x2 + 75x + 25000,
where x is the number of units produced. At what level of production will the average cost per unit be minimized? (The average cost per unit is C/x.)
x = units

x = 100 units

Step-by-step explanation:

C = 2.5x^2 + 75x + 25000

To find average cost per unit, divide C by x:

C/x or Average cost (AC) per unit = = 2.5x + 75 + 25000/x ⇔ 2.5x + 75 + 25000x^-1 (equation 1)

To find cost minimising, we use differentiation (differentiate equation 1 in respect to x and set it equal to 0):

d(AC)/dx = 0

d(AC)/dx ⇔ 2.5 - 25000x^-2 = 0

2.5 = 25000x^-2

2.5 =

2.5x^2 = 25000

x^2 = 10000

x =

x = 100 units

their is no graph showing

step-by-step explanation:

answer:   the paragraph proof is mentioned below.

step-by-step explanation:

given: in a δxwy where

such that, ∠wzx ≅ ∠yzx and zw≅zy

we have to prove that: segment zx is a perpendicular bisector of segment wy.

prove: since, zw≅zy ⇒ ∠wzy is a supplementary angle.

then, ∠wzy= 180°

⇒∠wzx + ∠yzx = 180° ( because xz divides ∠wzy into two parts)

but, ∠wzx ≅ ∠yzx ( given)

⇒∠wzy+∠wzy=180° ( by substitution)

⇒2∠wzy=180°

⇒∠wzy=90°

⇒∠wzy=∠yzx =90°

therefore, xz⊥wy where wz=zy

⇒zx is a perpendicular bisector of wy.