There are two $(2)$ problems in this homework. Although they are not graded, you are encouraged

to complete them as they will help you with the problem$-$based questions in your exams.

The intention of these problems is for you to practice, develop critical thinking and problem$-$solving skills.

Problem $1$:

Better Products, Inc., manufactures three products. Each product has to run through all three machines

sequentially. In a typical week, $36$ hours are available on each machine. The profit contribution and production

time in hours per unit are as follows:

Category Product $1$ Product $2$ Product $3$

Profit$/$unit $$30$ $$50$ $$35$

Machine $1$ time$/$unit $1\mathrm{.}251\mathrm{.}751$

Machine $2$ time$/$unit $1\mathrm{.}01\mathrm{.}00\mathrm{.}75$

Machine $3$ time$/$unit $0\mathrm{.}750\mathrm{.}751\mathrm{.}25$

Only one operator is required for machine $1.$ Two operators are required for machine $2$; thus, $2$ hours of labor

must be scheduled for each hour of machine $2.$ The same applies to machine $3$ which requires two operators to

operate this machine; hence, $2$ hours of labor must be scheduled for each hour of machine $3.$ A maximum of $148$

labor$-$hours is available for assignment to operators to work on the machines during the coming week.

Other production requirements are that product $1$ must account for at least $40\%$ of all units produced and product

$2$ cannot be more than $25\%$ of the units produced from products $1$ and $3.$

The company is interested in weekly profit. Using Excel Solver, develop the optimal product mix and answer the

following questions.

From your optimal solution, what is your product mix and its associate projected w