An industrial production process costs Cq thousands dollars

An industrial production process costs C(q) thousands dollars to produces q thousands units; these units then sell for R(q) thousands dollars. If C(230) = 490, R(230) = 800, MC(230) = 32, MR(230) = 25. Calculate (a) The prost earned by producing 230 thousand units. (b) The approximate change in profit if production increases from 230 to 20 thousand units. (e) The approximate change in profit if production decreases from 230 to 219 thousand units. (d) At the production level 230 thousand units, should the company increase or decrease production order to maximize the profit?

Solution

a)profit earned in producing 230 thousand units =R(230)-C(230)

profit earned in producing 230 thousand units =800-490

profit earned in producing 230 thousand units =310 thousand dollars

b)

approximate change in profit =25*(242-230) -32*(242-230)

approximate change in profit =25*(12) -32*(12)

approximate change in profit =300-384

approximate change in profit =-84

approximate change in profit is 84 thousand dollars

c)

approximate change in profit =25*(219-230) -32*(219-230)

approximate change in profit =25*(-11) -32*(-11)

approximate change in profit =-275+352

approximate change in profit =77

approximate change in profit is 77 thousand dollars

d)

at level of 230 thousand units,company should decrease production in order to maximise the profit