ABC company makes two types of kids toys: airplanes and cars. Each toy is produced in two stages, first it is constructed in a carpentry shop and then it is sent to a finishing shop, where it is polished. To make one toy airplane costs 10 USD for raw material and 14 USD for labor; it takes 1 hour in the carpentry shop, and 2 hours for finishing. To make one car costs 9 USD for raw materials and 10 USD for labor; it takes 1 hour in the carpentry shop and 1 hour for finishing.

There are 80 hours available each week in the carpentry shop, and 100 hours for finishing. Each toy airplane is sold for 27 USD while each car for 21 USD . Due to decreased demand for airplanes, the company plans to make and sell at most 40 toy airplanes; the number of cars is not restricted in any way.

Questions

Your task is to help the company find the optimum (best) product mix that maximizes the profit? To solve this problem, you must answer the following questions:

• Cleary spell out the decision variables and what they represent
• Formulate the constraints imposed by the problem
• Cleary spell out the objective function
• Write the complete mathematical model of this problem
• Solve this model using the graphing method
• Find the optimal solution(s) if they exist
• Interpret the results if any