Question

A farmers’ coop has 6000 ha available on which to plant maize and Bambara nuts. The following table summarises each crops requirements for fertilizer/herbicides, harvesting labour hours and the available amounts of these resources. Maize Bambara nuts Available resources Fertilizer/herbicide 9l/ha 3l/ha 40500l Harvesting labour 0.75hr/ha 1hr/ha 5250hr If the coops profits are N240/ha for maize and N$160/ha, using simplex method, how many ha of each crop should the coop plant i. To maximize profit (16) ii. How much is the profit 

Answer 1

Formulation of LPP is given by,

Maximize P=240x +160y

Subject to:

x+y≤6000 (Constraint for Land area)

9x+3y≤40.500 (Constraint for Fertilizer/herbicide)

(3/4)x +y≤5250 (Constraint for Harvesting labor)

x,y≥0