Exam $1($IE $535-$ Fall, $2023)$

Your Name:

$(13$ pt$)$ Suppose that a company produces two kinds of products, denoted as Product A and B$.$ Per unit

of Product A requires $2$ hours of assembly labor, $1\mathrm{.}5$ hours of testing, and $$1\mathrm{.}2$ worth of raw materials. Per

unit Product B requires $4$ hours of assembly labor, $2$ hours of testing, and $$0\mathrm{.}8$ worth of raw materials. The

company currently can have at most $100$ hours of assembly labor and $80$ hours of testing, on a daily basis.

Suppose that Product A has a market value of $$10$ per unit, and B has a market value of $$9$ per unit.

$(4.$a$)(8$ pt$)$ Formulate a linear programming problem to help the company determine how many units of

Product A and B to produce to maximize its daily profit, subject to all the described constraints. $($Please

ignore any integrality requirements.$)$