Questions:

1.

The market value of an asset, if it is sold at time t0, is assumed to be V(t)=(t+2)2. The present value P(t) of money raised if it is sold at time t is V(t)e0.1t.

Show that there is one critical point forP(t) fort0

Use the second derivative test to show thatP(t) is maximised at the critical value of t. Determine the maximum value of P(t), expressing your answer in terms of e.

2.

A company's production function is given by

Q=100[0.4K5/2+0.6L5/2]2/5

and input limitations mean that 16K+3L=134. Use the Lagrange multiplier method to find the values ofK andL that maximise the production function subject to the given constraint.