Gce Model Questions Vol1 2017 Agricultural Science Question 50

A mixed farm has 10 ha of land. Wheat yields 2.5 t ha\(^{-1}\) and sells for \$200 t\(^{-1}\). Each kilogram of wheat incurs a variable cost of \$30. Goats provide meat worth \$150 each; each goat requires 0.1 ha of grazing land and incurs a variable cost of \$40. Fixed annual costs (machinery, buildings) are \$5 000. The farm has 1 800 labour hours available per year; wheat requires 150 labour hours per hectare and each goat requires 20 labour hours. Let \(x\) be hectares planted to wheat and \(y\) the number of goats. Formulate and solve the linear‑programming problem to maximise annual profit, subject to the land and labour constraints. State the optimal values of \(x\) and \(y\) (to the nearest whole number) and the maximum profit (in dollars).