# Mathematics

Mathematics

This is due tonight at 10PM eastern standard time so i can review before submitting.

Tab 1

26) A furniture company manufactures desks and chairs.  Each desk uses 4 units of wood and each chair uses 3 units of wood.  The desk contributes \$400 to profit and a chair contributes \$250. Marketing restrictions require that the number of chairs produced be at least twice the numbers of desk produced.  There are 2000 units of wood avaliable.

(A) Use solver to maximize company profits.

(B) Confirm graphically that the solution in part A maximizes the companys profit

(C) Use solver table to see what happens to the decision variables and the total profit when the avaliability of wood varies from 1000 to 3000 in a 100 unit increments.  Based on your findings how much would the company be willing to pay for each extra unit of wood over its current 2000 units?  How much profit would the company lose if it lost any of its current 2000 units?

Tab 2

34) There are 3 factories on the Momiss River each emits 2 types of pollutants, labeled P1 and P2, into the river. If the waste from each factory is processed the pollution in the river can be reduced.  It cost \$1500 to process a ton of factory 1 waste, and each ton processed reduces the amount of P1 by 0.10 ton and the amount of P2 by 0.45 ton.  It cost \$1000 to process a ton of factory 2 waste and each ton processed reduces the amount of P1 by 0.20 ton and the amount of P2 by 0.25 ton.  It cost \$2000 to process a ton of factory 3 waste and each ton processed reduces the amount of P1 by 0.40 ton and the amount of P2 by 0.30 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.

(A) Use solver to determine how to minimize the cost of reducing pollution by the desired amounts, are the LP assumptions (proportionality, additivity, divisibility) reasonable in this problem?

(B) Use solver table to investigate the effects of increases in the minimal reductions required by the state.

Specifically see what happens to the amounts of waste processed at the 3 factories and the total cost if both requirements (currently 30 and 40 tons respectively) are increased by the same percentage.  Revise your model so you can use solver table to investigate these changes when the percentage increase varies from 10% to 100% in increments of 10% do the amounts processed at the 3 factories and the total cost change in a linear manner.

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