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.?

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Answer 1 · 2018-04-16T12:14:43

This is what I get

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^'#

#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)#, equals the number of plants sold. Therefore,

#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 #=# Marginal Revenue #–# Marginal Cost
Therefore, Marginal Profit function is

#3 -x/500-0.02#
#=>2.98 -x/500#
in the given interval.