A company is planning to manufacture and sell hair dryers. The price-demand and cost equations are estimated to be respectively; p(x) = 50 – 0.2x , C(x) = 5x + 1700 where x is the # of hair dryers that can be sold at a price of $p per hair dryer and C(x) is the total cost (in dollars) of producing x dryers.

A. Find the average cost function for ? televisions produced. B. Find the instantaneous rate of change of the average cost function.

The supply for a particular item is given by the function S(x) = 17 + 0.36x² . Find the producer's surplus if the equilibrium price of a unit $53. The producer's surplus is $

A family plan  for a cell phone has a monthly price of $75 plus $10.99 for each additional family member added beyond the primary account holder. The linear function to model the monthly cost C(x) in ($) of a family for x additional family members added is C(x)=

An electronics company is planning to manufacture a new line of high-end noise reduction ear buds. Fixed costs will be ​$123,000 and it will cost $13 to produce each pair of ear buds. The ear buds will sell for $43 a pair. Using the equations for cost C and revenue R as given below where x represents the units of​ product, find the​ break-even point for producing the new ear buds.   C(x)=fixed cost+(cost per unit produced)•x R(x)=(price per unit sold)•x What is the​ break-even point?

A cellular phone service provider charges $45 per month and $0.08 per minute of airtime. Enter the linear model that represents the monthly charge, c, as a function of t, the airtime used, in minutes. C (T)=

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…