A firm manufactures two products; the net profit on product 1 is Rupees 3 per unit and Rupees 5 per unit on product 2. The manufacturing process is such that each product has to be processed in two departments D1 and D2. Each unit of product1 requires processing for 1 minute at D1 and 3 minutes at D2; each unit of product 2 requires processing for 2 minutes at D1 and 2 minutes at D2. Machine time available per day is 860 minutes at D1 and 1200 minutes at D2. How much of product 1 and 2 should be produced every day so that total profit is maximum. Make the mathematical model for the given problem.

In a high school with 3000 students, counselors are putting together a math tutoring program for the neighboring middle school. they plan to invite high school students with high average test scores to tutor middle school students, and they would like to offer gift cards to the student tutors. the counselors have a spreadsheet showing each student’s average test scores, and in order to find out how many gift cards they should purchase, the counselors need to count how many students would qualify to become tutors. which type of function would best the counselors determine the number of eligible students?