# Homework Week 6

```Name _________________________________
Math 3 Homework Sheet
Monday, 9/10/12
1.
x  2
 y  2x  4

y  3

y   3 x  3

2
Graph the system of inequalities to the right.
Vertices (x,y)
4x  2 y
f ( x, y )
The maximum value is _________ at ______________.
The minimum value is _______ at __________.
Tuesday, 9/11/12
A farmer has 10 acres to plant in wheat and rye. He has to plant at least 7 acres. However, he has only \$1200 to
spend and each acre of wheat costs \$200 to plant and each acre of rye costs \$100 to plant. Moreover, the
farmer has to get the planting done in 12 hours and it takes an hour to plant an acre of wheat and 2 hours to
plant an acre of rye. If the profit is \$500 per acre of wheat and \$300 per acre of rye how many acres of each
should be planted to maximize profits?
Constraints:
Graph your system on a separate sheet of GRAPH PAPER!
Profit Equation:
Vertices:
Solution (with support)
Wednesday, 9/12/12
A company manufactures and sells two models of lamps, L1 and L2. To manufacture each lamp, the manual
work involved in model L1 is 20 minutes and for L2, 30 minutes. The mechanical (machine) work involved for
L1 is 20 minutes and for L2, 10 minutes. The manual work available per month is 100 hours and the machine is
limited to only 80 hours per month. Knowing that the profit per unit is \$15 and \$10 for L1 and L2, respectively,
determine the quantities of each lamp that should be manufactured to obtain the maximum benefit.