**EXPERT ANSWER**

Demand : P = 160 – 8Q

Cost : c = 120 – 6Q

a) Profit = Revenue – Cost

Revenue = P*Q = 160Q – 8Q^{2}

Profit : U = 160Q – 8Q^{2} – 120 – 6Q

= 154Q – 8Q^{2} – 120**Total profit function : U = 154Q – 8Q ^{2} – 120 **

b) Maximizing total profit :

dU/dQ = 154 – 16Q = 0

or, 16Q = 154

or, Q = 154/16

or, Q = 9.62 or 10 (rounded)

d^{2}U/dQ^{2} = -16 <1**Hence for Q = 10, profit will be maximum.**

c) Maximum profit will be obtained by the value U at of Q=10

Maximum Total profit : U = 154Q – 8Q^{2} – 120

= (154*10) – (8*10*10) – 120

= 1540 – 800 – 120

= 620

**Hence maximum value of profit = 620**