Acompany earns a weekly profit of p dollars by selling x items, according to the equation p(x)=-0.5x^2+40x-300 how many items does the company have to sell each week to maximize its profit

The company have to sell 40 items each week to maximize its profit.

Step-by-step explanation:

The given profit function is

            .... (1)

where, p is weekly profit in dollars and x is number of sold items.

In the given function leading coefficient is negative, it means it is a downward parabola and vertex of a down word parabola is point of maxima.

If a parabola is defined as

               .... (2)

then the function is maximum at .

From (1) and (2) we get

The given function is maximum at x=40.

Therefore the company have to sell 40 items each week to maximize its profit.

11. z = 32/5

12.  y =25

13. x = 11/5

Step-by-step explanation:

11.  z       8

  =

4             5

using cross products

z*5 = 4 * 8

5z = 32

divide by 5

z = 32/5

12.  9       15

  =

   15         y

using cross products

9* y = 15 * 15

9y = 225

divide by 9

9y/9 = 225/9

y =25

13.   11       5

      =

      x         1

using cross products

11*1 = 5x

divide by 5

11/5 = x