Burger Office Equipment produces two types of desks: standard and deluxe. Deluxe desks have oak tops and more expensive hardware, requiring additional time for finishing and polishing.

- Standard desks require 65 board feet of pine and 9 hours of labor.
- Deluxe desks require 50 board feet of pine, 25 square feet of oak, and 19 hours of labor.

For the next week, the company has the following resources available:

- 6,000 board feet of pine
- 750 square feet of oak
- 500 hours of labor

Profits:

- Standard desks net a profit of $240.
- Deluxe desks net a profit of $340.

All desks can be sold to national chains. After reviewing the hardware and labor requirements, along with the profit for each model, Burger Office Equipment developed a 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.

a. If 25% of the pine is deemed to be cosmetically defective, how will the optimal solution be affected?

- The optimal solution, when 25% of the pine is deemed to be cosmetically defective, is to produce $ S $ standard desk(s) and $ D $ deluxe desk(s).
- This solution gives the possible profit, which is $ P $.
- This solution is the same as the original solution because the number of standard desks produced has [unchanged/increased/decreased], the number of deluxe desks produced has [unchanged/increased/decreased], and the profit has [unchanged/increased/decreased].

Please refer to the accompanying linear optimization model for details.

In a mathematical optimization problem, if 25% of pine for Burger Office Equipment becomes defective, this reduces the total available to 4500 board feet. This will affect the production of both standard and deluxe desks, and potentially the total profit. A re-optimization would need to be made to allocate the reduced pine resource between the two types of desks.

This problem is essentially a problem of linear programming, a mathematical method for determining a way to achieve the best outcome such as maximum profit or lowest cost, in a given mathematical model for some list of requirements represented as linear relationships. The variable S represents the number of standard desks and D the number of deluxe desks produced.

Suppose that 25% of pine becomes cosmetically defective, this means that only 75% of it is usable. Therefore, the available board feet of pine decreases from 6000 to 6000*0.75 = 4500 board feet. This would limit the number of both standard and deluxe desks that Burger Office Equipment could produce, since both types of desks require pine.

We cannot determine the exact impact on the optimal solution without knowing the full specifics of the linear optimization model. However, generally, in such problems, a reduced supply of one resource (in this case, pine) would require a re-optimization of how that resource is allocated between the two types of desks. This can affect both the number of each type of desk that is produced and the total profit.

To know more about "Mathematical Model":

https://brainly.com/question/12914406

#SPJ11