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Burger Office Equipment 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 $=250S+350D$

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

$20D750(Availabilityof$ oak$)$

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

$S0$ and $D0$

b$.$ The shop supervisor is suggesting that the workforce be allowed to work an additional $50$ hours at an overtime premium of $$\frac{16}{?}$ hour. Is this a good suggestion? Why

or why not?

Since the cost of labor

a binding constraint, increasing the amount of labor

increase the number of units that could be produced. At an additional

cost of $$\frac{16}{?}$ hour for the overtime labor, the standard desks would

be profitable and the deluxe desks would

be profitable. Therefore, the

overtime

be a good suggestion.