A and B are two types of fertilizers available at Rs.30 per Kg and Rs.50 per Kg respectively. Fertilizer A contains 20 units of potash, 10 units of nitrogen and 40 units of phosphorous. Fertilizer B contains 15 units of Potash, 20 units of nitrogen and 10 units of phosphorous. The requirement of potash, nitrogen and phosphorous at least 1800, 1700,1600 units. Formulate the problems as L.P.P in order to minimize the total purchasing cost.
Answers
Given :
The cost of fertilizer A = Rs 30 per kg
The cost of fertilizer B = Rs 50 per kg
Fertilizer A contains
Potash = 20 units
Nitrogen = 10 units
Phosphorous = 40 units
Fertilizer B contains
Potash = 215 units
Nitrogen = 20 units
Phosphorous = 10 units
Total requirement of Potash = 1800 units
Total requirement of Nitrogen = 1700 units
Total requirement of Phosphorous = 1600 units
To Find :
Total purchasing cost
Solution :
Total quantity of potash including fertilizer A and B = 20 + 215 = 235 units
Total quantity of Nitrogen including fertilizer A and B = 10 + 20 = 30 units
Total quantity of phosphorous including fertilizer A and B = 40 + 10 = 50 units
And
Total cost of fertilizer A = ( 20 + 10 + 40 ) × Rs 30
= 70 × Rs 30
= Rs 2100
Total cost of fertilizer B = ( 215 + 20 + 10 ) × Rs 50
= 245 × Rs 50
= Rs 12250