A farmer wishes to plan production on his 200 acre farm over the next five years.[9]

At present he has a herd of 120 cows. This is made up of 20 heifers and 100 milk-producing cows. Each heifer needs 2/3 acre to support it and each dairy cow 1 acre. A dairy cow produces an average of 1.1 calves per year. Half of these calves will be bullocks which are sold almost immediately for an average of £30 each. The remaining heifers can be either sold almost immediately for £40 or reared to become milk-producing cows at two years old. It is intended that all dairy cows be sold at 12 years old for an average of £120 each, although there will probably be an annual loss of 5% per year among heifers and 2% among dairy cows. At present there are 10 cows of each age from newborn to 11 years old. The decision of how many heifers to sell in the current year has already been taken and implemented.

The milk from a cow yields an annual revenue of £370. A maximum of 130 cows can be housed at the present time. To provide accommodation for each cow beyond this number will entail a capital outlay of £200 per cow. Each milk-producing cow requires 0.6 tons of grain and 0.7 tons of sugar beet per year. Grain and sugar beet can both be grown on the farm. Each acre yields 1.5 tons of sugar beet. Only 80 acres are suitable for growing grain. They can be divided into four groups whose yields are as follows:

group 1	20 acres	1.1 tons per acre
group 2	30 acres	0.9 tons per acre
group 3	20 acres	0.8 tons per acre
group 4	10 acres	0.65 tons per acre

Grain can be bought for £90 per ton and sold for £75 per ton. Sugar beet can be bought for £70 per ton and sold for £58 per ton.

The labour requirements are:

each heifer	10 hours per year
each milk-producing cow	42 hours per year
each acre put to grain	4 hours per year
each acre put to sugar beet	14 hours per year

Other costs are:

each heifer	£50 per year
each milk-producing cow	£100 per year
each acre put to grain	£15 per year
each acre put to sugar beet	£10 per year

Labour costs for the farm are at present £4000 per year and provide 5500 hours labour. Any labour needed above this will cost £1.20 per hour.

How should the farmer operate over the next five years to maximize profit? Any capital expenditure would be financed by a 10 year loan at 15% annual interest. The interest and capital repayment would be paid in 10 equally sized yearly instalments. In no year can the cash flow be negative. Lastly, the farmer would not wish to reduce the total number of dairy cows at the end of the five year period by more than 50% nor increase the number by more than 75%.