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# Optimization

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There are three manufacturing plants on Lake Chinquapin: 1, 2, and 3. Each factory emits two types of pollutants, P1 and P2, into the water. If the waste from each factory is processed, the pollution in the lake can be reduced. It costs \$15 to process one ton of Factory 1 waste, and each ton processed reduces the amount of P1 by .10 ton and the amount of P2 by .45 ton. It costs \$10 to process one ton of Factory 2 waste, and each ton processed reduces the amount of P1 by .20 ton and the amount of P2 by .25 ton. It costs \$20 to process one ton of Factory 3 waste, and each ton processed reduces the amount of P1 by .40 ton and the amount of P2 by .30 ton. The state wants to reduce the amount of P1 in the river by at least 30 tons and the amount of P2 by at least 40 tons. Determine how to minimize the cost of reducing pollutants to the desired amounts.

-Confidence intervals and hypothesis testing
-Decision trees (and their use in solving managerial problems),
-Critical fractile analysis (and its use in determining optimal demand levels),
-Analysis of variance/ANOVA (and its use in understanding differences between group means),
-Chi-square (cross tabs/contingency table) analysis (and its use in determining differences between group proportions),
-Regression, single and multiple (and its use in understanding relationships between dependent and independent (explanatory) variables), and
-Optimization modeling (and its use in determining the best solution given a set of constraint).

https://brainmass.com/statistics/hypothesis-testing/optimization-11143

#### Solution Summary

Solution discusses that there are three manufacturing plants on Lake Chinquapin: 1, 2, and 3. Each factory emits two types of pollutants, P1 and P2, into the water. If the waste from each factory is processed, the pollution in the lake can be reduced. It costs \$15 to process one ton of Factory 1 waste, and each ton processed reduces the amount of P1 by .10 ton and the amount of P2 by .45 ton. It costs \$10 to process one ton of Factory 2 waste, and each ton processed reduces the amount of P1 by .20 ton and the amount of P2 by .25 ton. It costs \$20 to process one ton of Factory 3 waste, and each ton processed reduces the amount of P1 by .40 ton and the amount of P2 by .30 ton. The state wants to reduce the amount of P1 in the river by at least 30 tons and the amount of P2 by at least 40 tons. Determine how to minimize the cost of reducing pollutants to the desired amounts.

-Confidence intervals and hypothesis testing
-Decision trees (and their use in solving managerial problems),
-Critical fractile analysis (and its use in determining optimal demand levels),
-Analysis of variance/ANOVA (and its use in understanding differences between group means),
-Chi-square (cross tabs/contingency table) analysis (and its use in determining differences between group proportions),
-Regression, single and multiple (and its use in understanding relationships between dependent and independent (explanatory) variables), and
-Optimization modeling (and its use in determining the best solution given a set of constraint).

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