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Category: Math Homework
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Experience:  B.S. in Civil Engineering
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# Production Planning. The Bogard Corporation produces three

Production Planning. The Bogard Corporation produces three types of bookcases, which it sells to large office supply companies. The production of each bookcase requires two machine operations, trimming and shaping, followed by assembly, which includes inspection and packaging. All three types require 0.4 hours of assembly time, but the machining operations have different processing times, as shown below, in hours per unit:

Standard        Narrow      Wide

Trimmer              0.2                    0.4            0.6

Shaper                0.6                    0.2            0.5

Each machine is available 150 hours per month, and the current size of the assembly department provides capacity of 600 hours. Each bookcase produced yields a unit profit contribution as follows:                                       Standard            Narrow        Wide

Profit                     \$8                      \$6              \$10 .

What are the optimal production quantities for the company? What is the pattern in the optimal allocation?

Question #2:

1. Fertilizing the Lawn. The facilities manager at Oxbridge University is planning to apply fertilizer to the grass in the quadrangle area in the spring. The grass needs nitrogen, phosphorus, and potash in at least the amounts given in the following table.

MineralMinimum Weight (lb)
Nitrogen12
Phosphorus14
Potash18

Three kinds of commercial fertilizer are available, with mineral content and prices per 1,000 pounds as given in the following table. There is virtually unlimited supply of each kind of fertilizer.

FertilizerNitrogen Content (lb)Phosphorus Content (lb)Potash Content (lb)Price (\$)
A2010510
B105158
C151057

How much of each fertilizer should be purchased to satisfy the requirements at minimum cost?

If this can be completed by Thursday morning that is great......I seems a bit lengthy, but maybe easier than it looks as well.  If the price is too low we can work out a deal on the bonus, please let me know...

Thanks,

Misty :)

Hi,

Thank you for the new request, and thank you for the high rating and bonus on the previous question.

I can help you with this problem, but I need a little bit of information from you. There are a few different ways of approaching this problem. Since I'm not in your class, I don't know what has been covered, which makes it difficult to select a method that is appropriate for your course.

What have you covered in your course regarding these types of problems?

Thanks,

Ryan
Customer: replied 4 years ago.

HI Ryan,

We are just now covering this chapter....so far we have covered Linear and non-linear optimization the basics from the previous chapter....this begins chapter 11 with allocation models, covering models and blending models. Really the basics for Excel modeling. The following is a link to the online chapter......http://my.safaribooksonline.com/book/management/9780470530672/linear-optimization/linear_optimization

Thanks,

Misty :)

Hi Misty,

Ok, then. It would seem that your course feels that using Excel's Solver is appropriate. That spares us the tedious, gritty details of a matrix solution.

I'll write up an explanation of how the constraints and objective functions are obtained, and include a screenshot of the Excel Solver solution. If you want it, I can also post the Excel file itself.

I expect to have this posted for you later today, or tomorrow morning. Well before your Thursday deadline in any case.

Thanks,

Ryan
Customer: replied 4 years ago.

Thanks Ryan...and the Excel file is greatly appreciated!

Have a wonderful day:)

Misty

Hi Misty,

Ok, I'll include that too.

Hope you have a great day too!

Regards,

Ryan
Hi Misty,

Here are the solutions:

OptimizationProblems(Word)

OptimizationProblems(Excel)

Note: There are two sheets in the Excel file. Each problem is on its own worksheet. I wanted to combine them on one sheet, but doing so would have caused problems with the Solver application.