IE312 Spring2010Quiz 1solutionsmodified

# IE312 Spring2010Quiz 1solutionsmodified - Name IE 312 Quiz...

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IE 312 Quiz 1 Solutions (Total 100 pts.) 1) Use the method of steepest ascent to approximate the optimal solution to the following problem: Max Z= -(x 1 -2) 2 - x 1 - x 2 2 . Begin at the point of (2.5, 1.5). (30 pts.) f(x 1 , x 2 ) = [3 - 2x 1 -2x 2 ] (2.5, 1.5) = [-2, -3]. Find t to maximize f(t 0 )=f[(2.5,1.5)+t 0 (-2,-3)]=f[2.5-2t 0 , 1.5-3t 0 ] So, to find a new point solve max f(t 0 )= -(0.5 - 2t 0 ) 2 - (2.5 - 2t 0 ) - (1.5 - 3t 0 ) 2 t 0 0 f'(t 0 ) = 4(0.5 - 2t 0 ) + 2 + 6(1.5 - 3t 0 ) = 0 if 13 - 26t 0 = 0 or t 0 = .50 New Point = (2.5, 1.5) + .5 (-2, -3) = (1.5,0) Since (1.5, 0) = [0 0] we conclude the algorithm. So z=-1.75 2) A company manufactures two products. If it charges a price p i for product i, it can sell q i units of product i , where q 1 = 60-3p 1 +p 2 and q 2 =80-2p 2 +p 1 . It costs \$25 to produce a unit of product 1 and \$72 to produce a unit of product 2. How many units of each product should be produced to maximize profits? (30 pts.) Max z= (p 1 -25)(60 - 3p 1 + p 2 ) + (p 2 -72)(80 -2p

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## This note was uploaded on 04/07/2010 for the course ENGINEERIN 12 taught by Professor Who during the Spring '09 term at Kadir Has Üniversitesi.

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IE312 Spring2010Quiz 1solutionsmodified - Name IE 312 Quiz...

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