A company manufactures bicycles of two different kinds: road bikes and city bikes. The profit per road bike sold is $400, while the profit per city bike sold is $150. Both types of bicycles are made of aluminum, but city bikes, being much heavier, require more than road bikes, specifically, each city bike needs 10 pounds, while the road bikes need 4 pounds each. The company has a weekly aluminum supply of 200 pounds. The manufacturing of the two types of bikes is also different, with city bikes requiring 10 hours of unskilled work plus 2 hours of skilled work per bike, while road bikes require 6 hours of unskilled work and 6 hours of skilled work per bike. The company's unskilled employees can work for a maximum of 360 hours per week, while its skilled employees can work for 120 hours per week. Both types of bikes also require components that are manufactured by a third party, and in order to secure a good whole sale price the company must ensure that they buy a minimum of $1000 worth of components per week from their supplier. Each city bike requires $60 in components, while each road bike requires $200 in components.

The company wants to determine the optimal number of city bikes and road bikes to make each week, and has formulated their problem as a linear program:

max 400x + 150y s.t. 4x + 10y 200 6x + 10y 360

6x + 2y 120 200x + 60y 1000 x, y 0

(a) Explain in words what each of the following expressions represents: i. x

ii. 400x+150y iii. 6x + 10y 360 iv. 200x + 60y 1000

v. 6x+2y120