a$)(10$ marks$)$ Calculate total production cost of each skateboard model.

b$)(20$ marks$)$ What Production Strategy is Xavier pursuing? Calculate the MPS for both models and MRP for Bearings $($using time unit: day$).$

c$)(10$ marks$)$ Xavier is considering Make to Stock policy to balance their workload. Their current warehouse capacity is $50$ skateboards per time. When all parts are accounted for, assembly of a downhill skateboard takes $45$ minutes while a mini$-$cruiser takes $35$ minutes. They have $4$ skilled workers working $7$ hours a day, excluding break and lunch time. Xavier leaves both models to their retailers at the wholesale price of $300$$ per skateboard. Formulate a linear programming model so that Xavier can maximize their profit given the above constraints.