Inequalities ContinuesLinear programming, ConstraintsFeasible region, Objective Function, Maximum, Minimum, and Vertex

MATH II

EXAMPLE 1 Suppose your class is raising money for

the Red Cross. You make $3 on each basket of fruit and $5 on each box of cheese that you sell. How many items of each type must you sell to raise more than $100?

MATH II

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MATH II

EXAMPLE 2 JoAnn likes her job as a baby-sitter, but

it pays only $3 per hour. She has been offered a job as a tutor that pays $6 per hour. Because of school, her parents only allow her to work a maximum of 15 hours per week. How many hours can JoAnn tutor and baby-sit and still make at least $66 per week? How much does she make?

MATH II

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MATH II

EXAMPLE 3This year at the Dixie Classic fair small rides are $3 and large rides are $5. You do not want to spend more than $60 on tickets. How many small ride or large rides can you ride?

MATH II

EXAMPLE 4Angela works 40 hours or fewer per week programming computers and tutoring. She earns $20 per hour programming and $10 per hourtutoring. Angela needs at least $500 per week. Write a system of inequalities that represents the possible combinations of hours spentprogramming that will meet Angela’s needs.

MATH II

Linear Programming is used to find optimal solutions, such as maximum and minimum values.

Characteristics:1. Inequalities are the constraints (restrictions)2. Solution to the inequalities is called the feasible region3. Function to be maximized or minimized is the objective function Hint: The maximum and minimum values of the objective function ALWAYS occurs at the vertices of the feasible region.

Steps to Solving a Linear Programming Problem:1) Graph the feasible region.2) Find the coordinates of each vertex by solving the appropriate system, if necessary.3) Evaluate the Objective Function at each vertex.

MATH II

MATH II

A small company produces knitted afghans and sweaters and sells them through a chain of specialty stores. The company is to supply the stores with a total of no more than 100 afghans andsweaters per day. The store guarantees that they will sell at least 10 and no more than 60 afghans per day and at least 20 sweaters per day. The company makes a profit of $10 on each afghan and a profit of $12 on each sweater. How does the company maximize its profit?

An accounting firm charges $620 for a business tax return and $200 for an individual tax return. The firm has 800 hours of staff time and 144 hours of review available each week. Each business tax return requires 40 hours of staff time and 8 hours of review time. Each individual tax requires 5 hours of staff time and 2 hours of review time. What number of business and individual tax returns will produce maximum revenue?X = ________________________ y = ______________________Objective Function: ____________________________________Constraints: ________________________________

________________________________ ________________________________Corner Points Value_________________ _________________________ ________Sentence: ___________________________________________________________________

A school dietician wants to prepare a meal of meat and vegetables that has the lowest possible fat and that meets the FDA recommended daily allowances of (RDA) of iron and protein. The RDA minimums are 20 mg of iron and 45 mg of protein. Each 3-ounce serving of meat contains 45 grams of protein, 10 mg of iron, and 4 grams of fat. Each 1-cup serving of vegetables contains 9 grams of protein, 6 mg of iron, and 2 grams of fat. Let x represent the number of 3-ounce servings of meat, and let y represent the number of 1-cup servings of vegetables. What is the minimum number of grams offat?

MATH II