The demand equation for your company's virtual reality video headsets is p =  2,000 q0.3  where q is the total number of headsets that your company can sell in a week at a price of p dollars. The total manufacturing and shipping cost amounts to $100 per headset. (a) Find the weekly cost, revenue and profit as a function of the demand q for headsets. C(q)=  R(q)= P(q)= (b) How many headsets should your company sell to maximize profit? (Give your answer to the nearest whole number.) q =        headsets What is the greatest profit your company can make in a week? (Give your answer to the nearest whole number.) $   Second derivative test: Your answer above is a critical point for the weekly profit function. To show it is a maximum, calculate the second derivative of the profit function. P"(q)=  780q−0.7       Evaluate P"(q) at your critical point. The result is      , which means that the profit is      at the critical point, and the critical point is a maximum.

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