An industrial production process costs C(q) million dollars to produce q million
ID: 2833063 • Letter: A
Question
An industrial production process costs C(q) million dollars to produce q million units; these units then sell for R(q) million dollars.
If C(2.1) = 5.1, R(2.1) =6.6, MC (2.1)= 0.5, and MR (2.1) = 0.6, calculate the following.
a) The profit earned by producing 2.1 million units. The profit is 1.5 million dollars
b)The approximate change in revenue if production increases from 2.1 to 2.13 million units. The change in revenue is about 18 thousand dollars.
c) The approximate change in revenue if production decreases from 2.1 to 2.06 million units. The change in revenue is about _______________ thousand dollars.
d) The approximate change in profit (part b) is about ____________dollars, and the change in profit in (part c) is about ______________ dollars
Explanation / Answer
a)Profit(2.1)= Revenue(2.1)-Cost(2.1) = 6.6-5.1=1.5
b)Use linearization L(x) =F'(x)dx+F(x) R(2.14)=MR(2.1)(0.04)+R(2.1) 0.4*0.04 + 6.6=6.616
c)Use linearization L(x) =F'(x)dx+F(x) R(2.14)=MR(2.1)(0.04)+R(2.1) 0.4*(-0.03) + 6.6=6.588
d)We want change in cost for b) MC * dx 0.4*0.04 =0.016
for c) 0.4 -.03=-0.012