Dairy cows12 in most countries calve on a regular annual basis. Their milk output varies over the year accordingly, with a peak reached a few months after calving followed by a decline to almost zero in the tenth month. Knowing these facts, farmers in an agricultural cooperative are trying to plan calving months c = 1,c, 12 to make it easier to meet seasonal milk demands rd pounds in months d = 1,c, 12. Any milk produced beyond these demands must be sold on the bulk market at b per pound below the regular price. The annual cost mc of maintaining a cow calving in month c varies significantly over the year because low-cost grazing is available only in certain seasons. From scientific studies the farmers can estimate the yield pd, c pounds in demand month d per cow calving in month

c. Formulate an LP model to determine a minimum total cost calving schedule using the decision variables 1c, d = 1,c, 122 xc ! number of cows calving in month c yd ! pounds of excess milk produced in demand month d