Precalculus Section 3.4 Solve problems using linear programming The inequalities that describe all the conditions of a problem are called constraints.

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Precalculus Section 3.4 Solve problems using linear programming The inequalities that describe all the conditions of a problem are called constraints. A maximum or minimum value of a linear function in the form C = Ax + By (objective function) occurs at a corner of the feasible region. The set of all points that meet all the constraints is called feasible region.

Find the maximum and minimum value of the objective function P = 4x + 7y given the feasible region.

Find the maximum value of the function P = 5x + 8y given the constraints. x + 2y < 4 x + y < 3 x > 0 y> 0

A factory produces short-sleeved and long-sleeved shirts. A short-sleeved shirt requires 30 minutes of labor, a long-sleeved shirt requires 45 minutes of labor, and 240 hours of labor are available per day. The maximum number of shirts that can be packaged in a day is 400. If the profits on a short-sleeved shirt is $11 and the profit on a long-sleeved shirt is $16, find the maximum possible daily profit. ShortLongtotal labor packaging profit

Assignment Page 112 Problems 1,3,6,9,10,11a