A nursery determines the demand in May for potted plants is p=3-(x/1000). the cost of growing x plants is c(x)= 0.02x +4000, 0<x<6000. determine the marginal profit function.?
1 Answer
This is what I get
Explanation:
Cost function is given as
#c(x)= 0.02x +4000#
for#0" < "x" < "6000#
We know that Marginal cost is the derivative of the cost function. Therefore, Marginal cost
#c^'(x)= d/dx0.02x +4000#
#=>c^'(x)= 0.02#
Demand function is given as
#p=3-(x/1000)#
where#x# is the demand for potted plants at a given price,#p#
Revenue
#R(x)=x xx p#
#=>R(x)=x xx (3-(x/1000))#
#=>R(x)=3x -x^2/1000#
Now Marginal revenue is the derivative of the Revenue function. Therefore,
Marginal Revenue
#=R^'=d/dx(3x -x^2/1000)#
#=># Marginal Revenue#=3 -x/500#
Now, Marginal Profit
Therefore, Marginal Profit function is
#3 -x/500-0.02#
#=>2.98 -x/500#
in the given interval.