$[0\mathrm{.}28/1$ Points$]$

CAMMBA$412.$E$\mathrm{.}006.$

senior designers. Due to other project commitments, Lisa has a maximum of $50$ hours available to work on this project. Hourly wage rates are $$30$ for Lisa, $$25$ for David, and $$18$ for Sarah. David is assigned to the project, and $S$ is the number of hours Sarah is assigned to the project.$)$

$($b$)$ How many hours should be assigned to each graphic designer?

Lisa's Hours $x$ hours

David's Hours $$ hours

Sarah's Hours

$x$

hours

What is the total cost $($in dollars$)?$

$ $$

$($c$)$ Suppose Lisa could be assigned more than $50$ hours. What effect would this have on the optimal solution? Explain.

The shadow price for this constraint is $,$ since the constraint is $-$ Therefore, additional hours for Lisa will not

$$ change the solution.

$($d$)$ If Sarah were not required to work a minimum number of hours on this project, would the optimal solution change? Explain.

The shadow price for this constraint is $q,,$ since the constraint is not binding $.$ Therefore, assigning fewer hours to Sarah $$ change the solution.