The demand equation for your company's virtual reality video headsets is 1,500 p = g0.3 where g 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 $110 per headset. (a) Find the weekly cost, revenue and profit as a function of the demand q for headsets. C(q)= 110g R(q)= 1500g0.7 P(g)= 1500 g0. – 1109 (b) How many headsets should your company sell to maximize profit? (Give your answer to the nearest whole number.) q = 1845 V headsets What is the greatest profit your company can make in a week? (Give your answer to the nearest whole number.) $ E 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)= 86977 Evaluate P"(q) at your critical point. The result is negative , which means that the profit is concave down v at the critical point, and the critical point is a maximum.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.