A vehicle assembly plant can produce two types of vehicles: Passenger cars (PC) and light trucks (LT). Each LT can be sold for a profit of AED 30,000 and each PC for a profit of AED 10,000. The assembly plant can be operational up to 40 hours per week. It takes 6 hours to assemble a LT and 3 hours to assemble a PC. Market demand is such that the assembly plant must make at least three times as many PC as LT. An LT takes up four times as much storage space as PC. There is storage space to at most four LT’s each week.
Formulate this problem as a linear programming (optimization) problem to maximize profit. Clearly show and/or mark the decision variables, constraints, and the objective function.