Systems of Inequalities in Two Variables

Graph of an Inequality Systems of Inequalities Linear Programming … and why Linear programming is used in business and industry to maximize profits, minimize costs, and to help management make decisions.

1. Draw the graph of the equation obtained by replacing the inequality sign by an equal sign. Use a dashed line if the inequality is < or>. Use a solid line if the inequality is ≤ or ≥. 2. Check a point in each of the two regions of the plane determined by the graph of the equation. If the point satisfies the inequality, then shade the region containing the point.

Carson’s Metals mines two ores: X and Y. The company extracts minerals W and Z from each type of ore. It costs $50 per ton to extract 80 lb of W and 160 lb of Z from ore X. It costs $60 per ton to extract 140 lb of W and 50 lb of Z from Y. Carson’s must produce at least 4000 lb of W and 3200 lb of Z. How much of each ore should be processed to minimize cost? What is the minimum cost? Cost is minimized when tons of ore X and tons of ore Y are processed. Minimum cost is $1,

Text pg621/622 Exercises #8-14 even & 32