ALLOCATING A LIMITED INPUT

I.M. Farmer raises 3 irrigated crops but is facing a shortage of water. I.M. needs some help deciding how a limited amount of water should be allocated between the 3 different crops. Use the data in the table and the following prices to solve I.M.'s problem.

Water - $8.00 per acre-inch

Cauliflower - $18.00 per cwt.

Cabbage - $7.00 per cwt.

Broccoli - $25.00 per cwt.

Water (acre inches)	Production (per acre)			Marginal Value Product
	Cauliflower (cwt.)	Cabbage (cwt.)	Broccoli (cwt.)	Cauliflower	Cabbage	Broccoli
0	56.0	173.0	49.5	XXX	XXX	XXX
3	64.4	197.4	60.2	50.40	56.93	89.17
6	71.6	218.2	68.6	43.20	48.53	70.00
9	77.6	237.4	74.6	36.00	44.80	50.00
12	82.4	253.2	80.0	28.80	36.87	45.00
15	86.6	265.7	84.8	25.20	29.17	40.00
18	90.6	271.9	88.4	24.00	14.47	30.00
21	94.2	274.0	90.8	21.60	4.90	20.00
24	97.0	275.2	92.0	16.80	2.80	10.00
27	97.8	275.6	92.0	4.80	0.93	0.00
30	98.0	274.0	90.5	1.20	-3.73	-12.50

1. How many inches of water should be used on each enterprise to maximize total

profit if I.M. has an unlimited supply at $8.00 per acre-inch?

Cauliflower Cabbage Broccoli ___________

2. If water costs $15.00 per inch, how many inches should be used on each enterprise to maximize total profit?

Cauliflower Cabbage Broccoli __________

3. Now assume price is $8.00 but only 36 acre-inches are available. How should this amount of water be divided between the 3 crops?

Cauliflower Cabbage Broccoli ____________

4. Same situation as above but water is limited to 27 inches. How should this water be allocated?

Cauliflower Cabbage Broccoli ____________

5. If only 21 inches of water is available, how should it be allocated to maximize profit from this limited amount of water ?

Cauliflower Cabbage Broccoli ____________

II. A rancher has a limited amount of labor available. Careful observation has shown that the last hour of labor used on the wheat enterprise increased income by $14.20 while the last hour of labor used on the beef cow enterprise increased income by $3.30. Is this rancher allocating the limited labor in a way which maximizes profit? Why or why not? If not, what should be done to increase profit?