Review Worksheet P. 2

IV. On a rectangular coordinate system, graph the solution set of the given system: 1. y>x 2 -2 2. y > 0

and x + y S 2

y < x + 3 and 2y < 6 - x

3. -1 < x< 3

-2 < y < 5 and 5y > x+1 1

4. l < x + 3 < 3

and \

5. y < x3 + 4 and y > x2 + x - 6 6. y > x3 - 9x

7. y < x 2 + x - 2 and y < - x 2 + x + 12 V. On one set of axes graph each of the following inequalities. Then shade the region that satisfies all the inequalities. Label each corner point of this region with its coordinates. x>0

y^3

x+y<12

and 3 y - x < 1 2

VI. An automobile manufacturer makes automobiles and trucks in a factory that is divided into shops. Shop 1, which performs the basic assembly operation, must work 5 person-days on each truck but only 2 person-days on each automobile. Shop 2, which performs finishing operations, must work 3 person-days on each automobile or truck that it produces. Because of personnel and machine limitations, Shop 1 has 180 person-days available while Shop 2 has 135 person-days per week. If the manufacturer makes a profit of $400 on each truck and $250 on each automobile, how many of each should be produced to maximize profit?

A manufacturer of metal widgets makes two types, A and B. Each type A widget requires .5 hours of cutting, 1.5 hours of welding, and 1 hour of finishing. Each type B widget requires .5 hours of cutting, 1 hour of welding and 1.5 hours of finishing. Each day 15 hours of cutting, 36 hours of welding time, and 42 hours of finishing time are available. If the profits on a type A widget and a type B widget are $3 and $4 respectively, how many of each type of widget should be made each day to maximize the total profits?