Question

Macro farms Ltd can purchase two types of fertilizer which contain the following percentage

Nitrate Phosphates Potash TypeX185 2 TypeY3 2 5

For certain type of crop, the following minimum quantities (kg) are required

Nitrate Phosphate Potash

100 50 40

Type X cost GHS10 per kg and type Y cost GHS5 per kg. The company currently buys 1,000

kg of each type and wishes to minimize it expenditure on fertilizers.

Required

a. Construct a linear programming model for the above problem (5 marks)

(5 marks) (6 marks) (6 marks)

b. Solve the model graphically

Answer 1

Sol Let Company produce 'r ky of Typex fortilizeres and uy kg of Type y fortilizer. Let Z be the total cost to make xey. we have to minimize z. - So, Linear programing model is - Min 2 = loxt sy with constraints -! 18++ 3y > 100 5x + 2y > 50 2x + 5y yo eslooo ys1000 and x, y, as company must produce some quantity.

S SO yot A 30 o,log 20 B In 2.0 yo 50 OGO autsy yo satry=so 18x+3y=100 First plotting the equations roughly? 18x+ 3y =100 5n+2y =50 2x + 5y = 40 x = lood y = 1000 we check the cost on A, B, C, D points of the feasible region (shadad Areas ne, ly) 1oxo + 5x1 = 5 = 500 = 166 (Apbror) on Ble, you 10x + 5x 400 = 2500 = 119 1700+ 500 104 N on z 21 N on 2200 z 21 2 on D (20, 0) 10x20+5xo 2 200