Hw3_Sol - Math464 - HW 3 Due on Thursday, Feb 4 1 Linear...

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Unformatted text preview: Math464 - HW 3 Due on Thursday, Feb 4 1 Linear Optimization (Spring 2010) Brief solutions to Homework 3 1. We rewrite the second constraint for cash availability in the LP formulation (given in the solu- tions to Homework 1) as follows: max 3 x 1 + 3 . 4 x 2 (net profit) s.t. 3 x 1 + 4 x 2 20 , 000 (max machine hours) . 3 x 1 + 0 . 38 x 2 4 , 000 (cash available, including re-financing) x 1 ,x 2 (non-negativity) The line (equation) of the second constraint lies entirely above the line of the first constraint, which connects (6666 . 67 , 0) and (0 , 5000). In other words, the cash availability constraint is redundant . The feasible region is a triangle with origin and the above two points as vertices. The optimal solution is (6666 . 67 , 0), i.e., produce 6666 . 67 units of product 1 and none of product 2. The corresponding maximum net profit is $20,000. To model the situation where the machine hours could be increased by 2000 hours at the cost of $400, change the right-hand-side value of the first constraint to 22000, and that of the second constraint to 3600. The second constraint still remains redundant, and the optimal solution isconstraint to 3600....
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This note was uploaded on 02/15/2011 for the course EECS 6.231 taught by Professor Bertsekas during the Spring '10 term at MIT.

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Hw3_Sol - Math464 - HW 3 Due on Thursday, Feb 4 1 Linear...

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