Linear programming

Page of 5 ZOOM . Part IV: Linear Programming We use linear programming to find an optimum value (a maximum or minimum) for an objective function. If an optimum value exists, it occurs at the vertex (or corner point) of the region of feasible solutions. To Solve a Linear Programming Problem: Write the objective function and all necessary constraints. Graph the region of feasible solutions Identify all vertices (corner points). Find the value of the objective function at each vertex. The solutions is given by the vertex producing the optimal value. 7. Lisa has an online jewelry shop where she sells earrings and necklaces. She sells carrings for $30 and necklaces for $40. It takes 30 minutes to make a pair of earrings and 1 hour to make a necklace. Since Lisa ia a math tutor, she has only 10 hours a week to make jewelry. Also, she only has enough materials to make 15 total jewelry items per week. Lisa makes a profit of Sis on each pair of earrings and $20 on cach necklace. How many pairs of earrings and necklaces should Lisa make each week in order to maximize her profit, assuming she sells all her jewelry? a Set up variables: Det represent Let y represent b. Write a system of inequalities to represent the constraints. c. Graph the region of feasible solutions, d. Write the objective function