A companys market research department recommends the manufacture and marketing of a new headphone set for the iPhone XS.

After suitable test marketing, the research department presents the following demand function...

p = 75 - 2q

The financial department provides the cost function below...

C(q) = 82 + 17q

where $82 is the estimate of fixed costs (tooling and overhead) and $17 is the estimate of marginal costs per headphone set (materials, labor, marketing, transportation, storage, etc.).

Find the number, q, of units that produces maximum profit.

(Round to the nearest whole number.)