Ski Patrol

Problem Definition

Ski Patrol Ltd. manufactures two different models of snowboards branded Normal and Deluxe with a weekly production plan and inventory. They sell their material to local shops. The company obtains a profit of 300€ per Normal snowboard and 400€ per Deluxe snowboard. The manufacturing process consists of roughing and polishing. The Normal snowboard model requires 20 minutes of roughing and 2/3 minutes of polishing. The Deluxe snowboard model requires 40 minutes of roughing and 1 minute of polishing. The roughing equipment is available for 1000 minutes per week and the polishing equipment for 800 minutes per week. Ski Patrol has already signed a contract with a local shop called Downhill Racer to deliver 18 Normal snowboards per week.

Ski Patrol hires you to formulate a Linear Programming Problem to help them determine the best production mix to maximise benefits.

Write a CLP to maximise profits

Decision Variables

\(x_{1}\): Units of Normal snowboards per week

\(x_{2}\): Units of Premium snowboards per week

Objective Function

\(\max z = 300·x_{1} + 400·x_{2}\)

Constraints

\(20·x_{1} + 40·x_{2} <= 1000\) Roughing process time (minutes)

\(2/3·x_{1}+x_{2} <= 800\) Polishing process time (minutes)

\(x_{1} >= 18\) Contract (Demand) Units

\(x_{2} >= 0\) (Physical constraint)