10. An electric scooter manufacturer estimates that the cost C in dollars) of producing x scooters is given by C(x) = 600+ 0.05x + 0.0002x%. Find the production level, to the nearest
unit, that will minimize the average cost Č(x) per unit.
A. 1733 scooters
B.
1250 scooters
C. 600 scooters
D.
1500 scooters

A. 1733 scooters

Step-by-step explanation:

To get x for minimum value of C bar, set derivative = 0

We Find our x.

C(x) = 600+ 0.05x + 0.0002x^2

We need average cos per unit

So divide by x both sides

C(x) / x = 600/x + 0.05x + 0.0002x

c(x)/c = Ç(x)

Therefore, Ç(x) = 600/x + 0.05x + 0.0002x

Now differentiate both side with x

dÇ(x)/dx = 600/x^2 + 0 + 0.0002

To find x for minimum Ç(x)

Set dÇ(x)/dx = 0 => -600/x^2 + 0.0002 = 0

=> x^2 = 600/0.0002

x^2 =3000000

x = √3000000

x = 1732.05

x = 1733

(0,-3) see attached graph

step-by-step explanation:

a. to solve the system, graph the two equations.

x = y+3 becomes y=x-3 has m=1/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move up 1 unit and 1 unit to the right. plot a point and connect.

y=-4x+3 has m =-4/1 and b=-3. start at (0,-3) on the y-axis and plot a point. then move down four units and to the right 1 unit. plot a point and connect.

the solution is the point (x,y) where the two lines intersect. by the graph below it is (0,-3).

b. to solve by substitution, substitute y = -4x-3 into x= y+3

x= (-4x-3) +3

x=-4x

5x=0

x=0

now substitute x = 0 back in to find y.

y= -4(0)-3

y=0-3

y=-3

solution is (0,-3)

c. use elimination by adding the equations together.

x-y=3

4x+y=-3

5x=0

x=0

then substitute into one equation to find y.

y=-4(0)-3

y=-3