Application Problems 10 If an item is sold for 100 then 30 w

Application Problems 10). If an item is sold for $100, then 30 will be sold. For each $5 the price is reduced, the merchant will sell 3 additional items. USE AN EQUATION to determine the selling price that will maximize the merchant\'s revenue 11.) The population of a town is now 3200 people and is known to double every 10 years (a) Write a function that gives the population, P (t), after t years (b) How many years will it take for the population to reach 7000? (A formula will suffice.)

Solution

R(x)= (100-5x)(30+3x) = -15x²+150x+3000

Revenue is maximum at origin

x=-150/2(-15)= 5

So selling price, p(x)= 100-5(5)=$75