Creative Toys (CT) is a manufacturer of toys with an innovative product development team that designs new toys for children of 10 years old or younger. The team has just finished the design of three different remote control toy cars, that is Car-TA, Car-TB, and Car-TC There is an i electronic component, called EX-30, that is used in all three cars. Making one Car-TA requires three EX-30 components, while making one Car-TB and Car-TC require four and five EX-30 components, respectively. CT has an inventory of 180,000 EX-30 components to produce these cars. Cars components are made in the fabrication department. The fabrication department then send the finished parts to the assembly department, where the production of cars is completed. To start producing each car model, CT needs to set up its Fabrication and assembly departments for these new products. The setup operations costs are $10,000, $12,000, and $8,000 for Car-TA, Car-TB, and Car-TC models, respectively If the operations are set up to produce a car, it should produce at least 8000 cars to reach its break-even point and become profitable. The bottleneck resource in each department is workers Car-TA requires 5 minutes of worker time in the fabrication department, while Cart-TB requires 6 minutes in the fabrication department. This number is 5 minutes for Car-TC. All three types of cars have the same assembly time of 3 minutes in the assembly department. The fabrication department has 16 workers and the assembly department has 6 workers. Both departments work 8 hours a day and 25 days a month CT plans to sell Car-TA, Car-TB, and Car-TC for $138, $169, and $146, respectively. The production cost of one Car-TA is $54, which includes all costs such as overhead cost, cost of materials, and labor costs (working in regular hours) Production costs for Car-TB and Car-TC are $73 and $62, respectively. It is estimated the demand for Car-TA, Car-TB, and Car-TC are 10000, 13000, and 25000 units, respectively CT is planning to set up its operations to produce these cars next month Answer the following questions if the goal is to maximize the profit CT gets by producing and selling these cars next month a. Should CT make all three types of cars, or should it only produce one or two types? b. How many of each type should be produced under the optimal production plan next month? What is the total profit under this plan?