Dietmar is in the process of choosing a cell phone and a cell phone plan. The first plan charges 20¢ per minute plus a monthly fee of $25, and the second plan offers unlimited minutes for a monthly fee of $100. (a) Find a linear function f that models the monthly cost f(x) (in dollars) of the first plan in terms of the number x of minutes used. f(x) = (b) Find a linear function g that models the monthly cost g(x) (in dollars) of the second plan in terms of the number x of minutes used. g(x) = (c) Determine the number of minutes for which the two plans have the same monthly cost. min

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"(qg) 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…