Linear Programming

Mert Gezer owns $$iftD$$ng$,$ a bicycle shop in Bah$$ek$$y$,$stanbul$.$ Most of Mert's bicycle sales are customer

orders; however, he also stocks bicycles for walk$-$in customers. He stocks three types of bicycles$$road

racing, cross country, and mountain.

Mert purchases his bicycles from a local manufacturer at the following prices: road racing bike $12,000,$

cross$-$country bike $17,000,$ and mountain bike $9,000.$ He has $120,000$ available this month to

purchase bikes. He sells road racing bikes for $18,000,$ cross$-$country bikes for $21,000,$ and mountain bikes

for $12,000.$

Each bike must be assembled; a road racing bike requires $8$ hours to assemble, a cross$-$country bike requires

$12$ hours, and a mountain bike requires $16$ hours. He estimates that he and his employees have $120$

hours$/$month available to assemble bikes.

Mert plans to stock at least as many mountain bikes as the other two combined because mountain bikes sell

better. He has enough space in his store to order $20$ bikes this month, and, based on past sales, Mert is

confident that he will be able to sell every bicycle.

Write a linear programming formulation of the problem using the outline provided below:

Decision variables $($explain your decision variables in detail$).$

Objective function $($expressed in terms of the decision variables$).$

Constraints $($expressed in terms of the decision variables$).$