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# Provides a report on Linear programming which comprises of:

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Provides a report on Linear programming which comprises of:
Abstract
History
Need few solved problems
Bibilography and References taken.

https://brainmass.com/math/linear-programming/provides-a-report-on-linear-programming-which-comprises-of-113262

#### Solution Preview

Linear programming
Need:
Abstract
History
Need few solved problems

Bibilography and References taken.

Abstract
In mathematics, linear programming problems are optimization problems in which the objective function and the constraints are all linear. The model was developed during the second world war by a number of researchers. Linear programming is heavily used in many different fields, either to maximize the income or minimize the costs of a production scheme.

History
Linear programming was a mathematical model developed during the second world war to plan expenditures and returns such that it reduces costs to the army and increases losses to the enemy. It was kept secret until 1947. Postwar, many industries found its use in their daily planning.
The founders of the subject are George B. Dantzig, who published the simplex method in 1947, John von Neumann, who developed the theory of the duality in the same year, and Leonid Kantorovich, a Russian mathematician who used similar techniques in economics before Dantzig and won the Nobel prize in 1975 in economics. A breakthrough came after 1947 when Fiacco and McCormick introduced the Interior Point Method in 1984.
Dantzig's original example of finding the best assignment of 70 people to 70 jobs still explains its success. The computing power required to scan all the permutations to select the best ...

#### Solution Summary

The solution provides detailed explanations and answer for the problem.

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## Quantitative Analysis (Decision Methods)

I got these problems wrong on a recent quiz...& I need thorough explanation and solution(s); so that I can use for reference in studying for the final examination. I'm really not understanding the logic & thought processes.

Thank you.

(See attached file for full problem description)

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1. ArtOrgan, Ltd. distributes replacement units for human mitral heart valves. Their forecast sales, at a price of \$7,900 per unit, is 12,500 units. ArtOrgan's cost is \$5,900 per unit. The cost of ordering is \$75 per order and the average carrying cost per unit per year works out to be about 5% of the cost of the valve. Lead time is 4 working days. Determine, based on 250 working days per year:

(a) the economic order quantity
(b) the optimal number of orders per year
(c) the reorder point

If demand variability during lead time is normally distributed with a standard deviation equal to 10% of the mean:

(d) what percentage of the order cycles will result in at least one stockout?
(e) what amount of safety stock would be required to provide 95% coverage?

2. As a supervisor of a production department, you must decide the daily production totals of a certain product that has two models, the deluxe and the special. The profit on the deluxe model is \$12 per unit, and the special's profit is \$10. Each model goes through two phases in the production process, and there are only 100 labor-hours available daily at the construction stage and only 80 labor-hours available at the finishing and inspection stage. Each deluxe model requires 20 minutes of construction time and 10 minutes of finishing and inspection time. Each special model requires 15 minutes of construction time and 15 minutes of finishing and inspection time. The company has also decided that the special model must comprise at most 60 percent of the production total.

(a) What is the best production strategy?
(b) What is the profit from the best strategy?
(c) If another worker is hired, to which department would you assign him?
Why?

How would your answers to (a) and (b) be affected if you discovered that the "specials" could only be sold by cutting their profit contribution to \$8?

(d) before your production plan was established and executed?
(e) after your production plan was established and executed?
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(See attached file for full problem description)

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