The cost, in millions of dollars, for a company to manufacture x thousand speed boats is given by the function c(x) = 3x2 - 30x + 175. find the number of speedboats that must be produced to minimize the cost.

  5000

Step-by-step explanation:

In vertex form, the cost function is ...

  C(x) = 3(x² -10x) +175 = 3(x² -10x +25) +175 -3(25)

  C(x) = 3(x -5)² +100

The vertex is at x=5, so the cost function will be minimized when 5000 speed boats are produced.

step-by-step explanation:

the system of inequalities is

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

the equation of the dashed line is

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

the equation of the solid line is

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

step 3

the system of inequalities is