Math 141 Quiz 3 Print Name__________________________

Section or class time___________________

1. a) A region is bounded by . Graph the region and label the corners.

b) Find the maximum and minimum and the points where they are attained for

P=

2. a) Graph the region, S, defined by . Label all corner points.

Is S bounded or unbounded?

b) Does have a maximum on S? If not, why not. If yes, where is it attained?

c) Does C=7x+8y have a minimum on S? If not, why not. If yes, where is it attained?

3. a) A carpenter and his son are building two models of tables. Table I uses 12 hours of carpentry, 5 hours of finishing, and $15 for wood. Table II uses 6 hours of carpentry, 5 hours of finishing and $25 for wood. They can work 120 hours in carpentry and 60 hours in finishing. They have $250 for wood. Each table I sells for $500 and each table II sells for $400. Find how many of each they should make to maximize their revenue. Are there any leftover resources? If so what and how much? Define all variables.

b) Re-work the problem if each table I is sold for $600 and each table II for $300. Give 3 solutions which maximize revenue and the leftover resources for each.