Question

A music store can stock 28,000 CDs at most. The store's manager wants to stock at least twice as many 4. rock CDs as rap CDs and have at least 2,400 country CDs in stock. The profit is $3 for a rock CD, $2 for a rap CD, and $3.50 for a country CD. How many of CDs of each type should the store have in stock in order to maximize profits? Set up the appropriate the linear programming problem to answer the problem, carefully defining each variable. (Do NOT solve the LP problem.)

Answer 1

let x is the number of rock CDs

y is the number of rap CDs

z is the number of country CDs

Max P = 3x + 2y + 3.5z

constraints are :-

x >= 2y

z >= 2400

x + y + z <= 28000

x , y , z >= 0

according to constraints the number of country cd can be greater than 2400

and the profit is maximum for country cd = $3.5 per cd

so if the stock can have atmost 28000 cd each of these can be country cd

so, z = 28000 and x , y = 0 will maximize the profit i.e

Max P = 28000 * 3.5 = $ 98000

Thus , to maximize profit the store should have 28000 country cd in stock