Answer to Question #162738 in Quantitative Methods for Sunny

Question

Fresh and farms company wishes to prepare a supply of special fertilizer at a minimal cost by mixing two fertilizer, A and B. The mixture is to contain at least 45 units of phosphate at least 36 units of nitrate at least 40 units of ammonium. Fertilizer A costs the shop Rs 50.00 per kg and fertilizer b cost the shop Rs 65 per kg. Fertilizer A contains 10 units of phosphate and 4 units of nitrate and 4 units of ammonium while fertilizer B contains 5 units of phosphate and 6 units of nitrate and 10 units of ammonium. How many units of each fertilizer should the firm use in order to minimize their cost? Use graphical method to solve the linear programming problem.

Answer 1

$x$ is the number of kg of fertilizer A, $y$ is the number of kg of fertilizer B.

Constraints:

$x\geq0,y\geq0$

$10x+5y\geq45$

$4x+6y\geq36$

$4x+10y\geq40$

Objective function:

$50x+65y\to min$

Corner points: $(0,9),(2.25,4.5),(7.5,1),(10,0)$

Minimum of objective function will be at point $(2.25,4.5)$, (2.25 kg of fertilizer A, 4.5 kg of fertilizer A):

$Cost_{min}=50\cdot2.25+65\cdot4.5=Rs\ \ 405$