### Projects (1999 - Spring 2008)

Engineering >> Industrial & Management Systems

## by Andrea Arnstein

Submitted : Fall 2013

The objective of this problem was to successfully maximize a company’s annual profit by optimizing the production of three independent products A, B, and C while dealing with storage and production constraints. To optimize these outcomes, a cost equation, annual profit equation, and constraint equation had to be formulated and utilized. Products A, B, and C had to be converted to NA, NB, and NC in order to account for the full years production (600 shifts / year). In order to account for the cost and annual profit equations, the cost of the material, the cost to make each product, and the given cost of the equipment to construct each product yearly became the cost equation and that was subtracted from the price that each product would sell for. The final annual profit equation after conversion and manipulation was = 1200NA - 200NA1.2 + 1800NB - 400NB1.2+ 2400NC -600NC1.2.

To account for the other constraint, I took the companies storage constraint per shift along with the size of each product and solved for the variable NC, doing this NC became 1250 – ½ NA – ¾ NB. Substituting NC into the final annual profit equation as listed above, I then solved for the partial derivative of NA and NB.

The partial derivatives being:

d/dNA = 360NC0.2-240 NA0.2, d/dNB = 540NC0.2-480 NA0.2

I then set each equation equal to zero and solved for an equation of NC. I then solved for NA and NB by comparing the equations to one another and solving for a common variable, and then I solved for NC. The final numbers for NA, NB, and NC was 1541.88, 367.361, 203.885 (units / shift) respectively.

In reference to the annual profit, I took the numbers found for NA, NB, and NC and inserted them into the final annual profit equation and found that the annual profit for the company would be \$828,953.005. For the floor usage each value of NA, NB, and NC multiplied by the products production space and was compared against the whole storage area (5000ft2) and the percentages were found. The floor usage of NA was 61.65%, NB was 22.04%, and NC was 16.311%.

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 Advisors : Brian Curtin, Mathematics and Statistics Scott Campbell, Chemical & Biomedical Engineering Suggested By : Scott Campbell