Question

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. Write the manufacturing constraint inequality.

Solution

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Let:

x = number of cell phone cases

y = number of tablet cases

Identify the variables:

Number of hours to manufacture cell phone case = 0.3

Number of hours to manufacture tablet case = 0.4

Maximum number of hours per day to manufacture = 8

Write the manufacturing constraint inequality:

0.3x + 0.4y $\leq$ 100, x $\geq$ 0 and y $\geq$ 0

The total number of hours (0.3x + 0.4y) to manufacture the cell phone and tablet cases per day should not be greater than 8. Of course, the number of cell phone and tablet cases should not be negative. Thus, x $\geq$ 0 and y $\geq$ 0.

Answer: 0.3x + 0.4y $\leq$8, x $\geq$ 0 and y $\geq$ 0

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