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Assignment (1)

Assignment (1). Week (4). Example (1). A farmer has 2400 ft of fencing and wants to fence off a maximize the rectangular field that borders a straight river. He needs no fence along the river. Formulate the optimization problem. Solution.

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Assignment (1)

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  1. Assignment (1) Week (4)

  2. Example (1) • A farmer has 2400 ft of fencing and wants to fence off a maximize the rectangular field that borders a straight river. He needs no fence along the river. Formulate the optimization problem.

  3. Solution • To solve the problem, we first draw a picture that illustrates the general case: • The next step is to create a corresponding mathematical model: Maximize: A = xy Subject to : 2x + y = 2400 X and y ≥ 0

  4. Problem (2) • We want to construct a reactortwhose base length is 3 times the base width. The material used to build the top and bottom cost $10/ft2and the material used to build the sides cost $6/ft2. If the reactor must have a volume of 50 ft3if you need to minimize the cost to build the reactor. Formulate the optimization problem

  5. Solution • We first draw a picture: • The next step is to create a • corresponding mathematical model: Minimize: C = 10(2lw) + 6(2wh + 2lh) = 10(2 · 3w · w) + 6(2wh + 2 · 3w · h) = 60w2 + 48wh Subject to : lwh = 3w2h = 50 w and h ≥ 0

  6. Problem (3) • A printer needs to make a poster that will have a total area of 200 in2 and will have 1 in margins on the sides, a 2 in margin on the top and a 1.5 in margin on the bottom. • What dimensions of the poster will give the largest printed area?

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