Rite cut riding lawnmower obeys the demand equation p=-1/20x+1060. the cost of producing x lawnmowers is given by the function c(x)=120x+5000

a)express the revenue r as a function of x
b)express the profit p as a function of x
c)fine the value of x that maximizes profit. what is the maximum profit?
d)what price should be charged to maximize profit?

answer:

given the linear inequality :

add 2y to both sides we get;

simplify:

add 12 to both sides of an equation;

simplify:

divide both sides by 2 we get;

or

the related equation for the inequality equation [1] is;

y-intercepts defined as the graph crosses the y-axis.

substitute x =0 in [2] to solve for y;

y = 6

x-intercepts defined as the graph crosses the x-axis.

substitute value y = 0 to solve for x;

subtract 6 from both sides we get

multiply both sides by 2 we get;

or

x = -12

now, plot these point (0, 6) and (-12, 0) on graph as shown below and shade the graph below the solid line.