Linear Programming

LINEAR PROGRAMMING APPLICATIONS OF INEQUALITIES

WRITE AN INEQUALITY FOR EACH OF THE CONDITIONS GIVEN. THEN GRAPH THE INEQUALITIES:

1. MWSS must supply at least 8 million gallons of water per day (mgd) to Quezon City. The water will come from the local reservoir or from a pipeline to a water supply located in the mountains. The local reservoir has a local yield of 4 mgd, which may not be exceeded. The pipeline can supply no more than 8 mgd. However, in order to use the pipeline, the company must agree to use a minimum of 6 mgd. What are the possible amounts from each source that will satisfy these conditions?

2. The Math Club decides to raise money by selling pencils. They order 300 blue and 400 red pencils. They must sell 100 pencils to break even. Each of the twenty students agrees to sell at least 10 pencils. If the club sells 200 blue pencils and 300 red pencils, have they satisfied all of the conditions? If they sell the pencils at Php10 and Php 20 for blue and red respectively, what is their maximum profit?

3. A summer program requires a minimum of 20 faculty members compose of teachers and assistants. At least 12 teachers are needed to run the program. For a proper teacherassistant-ratio, the number of assistants must be no more than twice the number of teachers, but there can be no more than 50 faculty members altogether. Can the school hire 12 teachers and 5 assistants?

4. The T.H.E. Club will sell rolls of wrapping paper and ribbon as a fundraiser. They can order up to 300 items, as long as they spend less than Php 600. They also must buy at least as many rolls of wrapping paper as rolls of ribbon. Each roll of wrapping paper costs Php 2 and each roll of ribbon costs Php 3. If the club buys 150 rolls of wrapping paper and 100 rolls of ribbon, will all the conditions be satisfied?

5. Graph each system of inequalities and give the coordinates of each corner point. a. x – y ≤ 1 x + 2y > 1 y< 1 b. x > 0 2y + x ≤ 6 x + 2 ≤ 2y