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Burger OffICE quipment produces two types of desks, standard and deluxe. Deluxe desks have oak tops and more$-$expensive hardware and require additional time for finishing and

polishing. Standard desks require $70$ board feet of pine and $11$ hours of labor, whereas deluxe desks require $55$ board feet of pine, $20$ square feet of oak, and $18$ hours of labor. For

the next week, the company has $5000$ board feet of pine, $750$ square feet of oak, and $400$ hours of labor available. Standard desks net a profit of $$250$ and deluxe desks net a profit

of $$350.$ All desks can be sold to national chains. After reviewing the hardware and labor required, along with the profit for each model, Burger Office Equipment found the

accompanying linear optimization model for profit, where $S$ is the number of standard desks produced and $D$ is the number of deluxe desks produced. Complete parts a through $d,$

answering each question independently relative to the original problem.

Click the icon to view the linear optimization model.

Linear Optimization Model

Maximize Profit $=250S+350D$

$70S+55D5000(Avallabilityof$ pine$)$

$20D750(Availabilityof$ oak$)$

$11S+18D400(Availabilityof$ labor$)$

$S0$ and $D0$

a$.$ If $20\%$ of the pine is deemed to be cosmetically defective, how will the optimal solution be affected?

The optimal solution when $20\%$ of the pine is deemed to be cosmetically defective is to produce standard desk$($s$)$ and deluxe desk$($s$).$ This solution gives the

$($Type integers or decimals rounded to two decimal places as needed.$)$