A car manufacturer produces two types of vehicles (Model X and Model Y) using three types of machines. The time required to produce the vehicles on each machine and the production cost per vehicle are given in the following table. Machine Production Assembly Pressing Production cost per car Model X Model Y Total Machine Time Available per Week 2.5 2.0 1,500 3.0 . 5.0 2,000 2.5 $15,000 1.5 $10,000 1,500 Each Model X sells for $55,000 and Model Y sells for $30,000. Management has determined that at least 20% of the vehicles made should be Model Y. How many of each model should the company produce if it wants to maximize its profit? Please formulate an LP model by (1) defining your decision variables, (2) using those variables to express the objective and constraints for this problem (do NOT solve it).