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# as6 - If it uses the legally permitted maximum of one unit...

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ECON 331 Written Assignment 6 due in class Oct. 28 1. A large firm controls three factories. The input and output levels of each factory are given by one column of the following matrix (inputs negative,outputs positive). factory a b c good1 1 0 -.5 good2 -2 3 2 good3 0 -.5 2 good4 1 3 -2 good5 1 -2 -1 If the prices of the five goods are given by 2 3 5 4 6 find the total profit of the firm. Write down a single matrix formula which represents how you have done this calculation. 2. A refinery can convert one unit of crude oil into three grades of gasoline. If it does not use lead additives it obtains the amounts of the three grades given by 4 2 2
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Unformatted text preview: . If it uses the legally permitted maximum of one unit of additives it obtains the amounts 3 0 5 . Assuming that the refinery can treat or not treat any amounts of crude oil it likes, can the company produce the following quantities of the three grades? (a) 11 4 9 (b) 10 3 12 3. Find the row vector x such that A x c T d where A 1 2 1 3 , A 1 3 2 1 1 , c T 2 2 , d 3 1 The matrix A 1 has the properties that A 1 A AA 1 A 1 T A T A T A 1 T 1 0 0 1...
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