14111cn3.7-9

# 14111cn3.7-9 - Minimize C = 44,000 x 54,000 y Subject to 60...

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Method of Corners: 1. Graph the corresponding equations by hand or on your calculator (i.e. solve each inequality for y and replace the inequality sign with an equal sign). Be careful in choosing your window. If there are non-negativity constraints on x and y , account for these by choosing x -min and y -min to be 0. 2. Determine the feasible region. 3. Find the coordinates of the corner points. You can either do this algebraically or on the calculator. There are four possible corner points: The origin (i.e the point ( 0 , 0 ) ) The intersection of two lines (use 2nd TRACE 5:intersect) The intersection of a line and the y -axis (recognize that this is the y -intercept of the line or use 2nd TRACE 1:value and enter in 0 for x ) The intersection of a line and the x -axis (plug in 0 for y and solve for x or use 2nd TRACE 2:zero and specify a left and right bound that includes the point where the line actually crosses the x -axis) 4. Make a table and evaluate the objective function at each corner point. Example 2:

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Unformatted text preview: Minimize C = 44,000 x + 54,000 y Subject to 60 x + 40 y ≥ 240 96 x + 160 y ≥ 672 x ≥ , y ≥ 7 Example 3: Solve the following linear programming problem Minimize P = 2 x + 2 y Subject to 2 x + 3 y ≤ 30 y-x ≤ 5 x + y ≥ 5 x ≤ 10 x ≥ , y ≥ 8 Example 4: You manage an ice cream factory that makes two ﬂavors: Vanilla and Mocha. Each quart of Vanilla requires 2 eggs and 3 cups of cream. Each quart of Mocha requires 1 egg and 3 cups of cream. You have in stock 500 eggs and 900 cups of cream. You make a proﬁt of \$3 on each quart of Vanilla and \$4 on each quart of Mocha. a) How many quarts of each ﬂavor should you make in order to earn the largest proﬁt? b) Are there any leftover resources? Be speciﬁc. • Keep the following in mind: Section 3.3 Highly Suggested Homework Problems: 3, 5, 15, 23, 25, 29, 31, 35, 39, 43 9...
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