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Find the vertices of the region.

COPY. ET 7.6. List the steps for solving a linear programming problem:. 1. Sketch the region corresponding to the system of constraints. The points inside or on the boundary of the region are the feasible solutions. 2. Find the vertices of the region.

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Find the vertices of the region.

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  1. COPY ET 7.6 List the steps for solving a linear programming problem: 1. Sketch the region corresponding to the system of constraints. The points inside or on the boundary of the region are the feasible solutions. 2. Find the vertices of the region. Test the objective function at each of the vertices and select the values of the variables that optimize the objective function. For a bounded region, both a minimum and a maximum value will exist. For an unbounded region, if an optimal solution exists,it will occur at a vertex. 3.

  2. A candy manufacturer wants to maximize the profit for two types of boxed chocolates. A box of chocolate covered creams yields a profit of $1.50 per box, and a box of chocolate covered nuts yields a profit of $2.00 per box. Market tests and available resources have indicated the following constraints. x = # of boxes of choc. creams y = # of boxes of choc. nuts The combined production level should not exceed 1200 boxes per month. 1. x + y < 1200 y < - x + 1200 The demand for a box of chocolate covered nuts is no more than half the demand for a box of chocolate covered creams. 2. y < ½ x The production level for chocolate covered creams should be less than or equal to 600 boxes plus three times the production level for chocolate covered nuts. 3. x < 600 + 3y y > 1/3 x - 200

  3. y < - x + 1200 y < ½ x y > 1/3 x - 200 Box Creams $1.50 Profit Box Nuts $2.00 Profit Maximum Profit (800, 400) 400 300 200 100 (0, 0) $ 0 (600, 0) $ 900 Boxes of Choc. Nuts 400 800 1200 (800, 400) (1050, 150) $ 2000 (1050, 150) $ 1875 (600, 0) (0, 0) Boxes of Choc. Creams

  4. Assignment 7.6 • Day 1: 40, 42,43, 45

  5. #40 (0, 0) (0, 1200) (4000/7, 6000/7) (1000, 500) (1250, 0) $0 $62, 400 $73, 142.86 $76,000 $62,500

  6. #42 (0, 0) (100, 0) (0, 120) (60, 90) (75, 75) $0 $14,000 $28,200 $29,550 $28,125

  7. #43 (0, 12) (3, 6) (9, 2) (18, 0) $240 $195 $265 $450

  8. #45 (0, 0) (12, 0) (5, 42) (0, 62) $0 $30,000 $27,200 $21,700

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