1. Think Break #8
Repeat the previous problem, but now use a milk price of Milk $10/cwt
M = – G H – G2 – H2 – GH
Prices: Grain $3/cwt, Hay $1.50/cwt
What are the profit maximizing inputs?

2. Think Break #8: Answer
p = 0.1(– G H – G2 – H2 – GH) – 0.03G – 0.015H
FOC’s
pG = 0.1(2.56 – G – H) – 0.03 = 0
pH = 0.1(1.05 – H – G) – = 0
2.56 – G – H = 0.03/0.10 = 0.3
1.05 – H – G = 0.015/0.10 = 0.15

3. Think Break #8: Answer Solve FOC1 for H
2.56 – G – H = 0.3
H = 2.26 – G
H = (2.26 – G)/
H = 642 – 2.87G
Substitute into FOC2 and solve for G
1.05 – H – G = 0.15
0.9 = (642 – 2.87G) G
0.9 = 1.4 – G G
– 0.5 = – G
G = 0.5/ = lbs/week

4. Think Break #8: Answer Substitute into equation for H H = 642 – 2.87G
H = 642 – = lbs/week
M = – G H – G2 – H2 – GH
M = – (182.5) (118.2) – (182.5)2 – (118.2)2 – (182.5)(118.2) = 306 lbs/week
p = 0.1(306) – 0.03(182.5) – 0.015(118.2) = $23.35/week