A group of college students are starting a small business called Custom Tech. They make customized cell phone and tablet cases. Their profits are $40 for the cell phone case and $60 for the tablet case. The process involves both design hours and manufacturing hours. It takes 0.5 hour to design and 0.3 hour to manufacture a customized phone case. It takes 0.4 hour to design and 0.4 hour to manufacture a customized tablet case. Since the design part is completed by students attending school, they can allocate no more than 100 hours per day for design. They are sharing a single manufacturing machine with another company and only have 8 hours per day to use it. Let x represent the number of customized cell phone cases and y represent the number of customized tablet cases.
a. Write the profit objective function.
b. Write the design constraint inequality.
c. Write the manufacturing constraint inequality.
d. Graph the constraint inequalities. Identify the coordinates of the feasible region.
How many of each type of customized case must they sell to maximize their profits?