A Pharmaceutical company produces two chemicals X and Y, such that X consists of 5% salt A and 10% salt B and Y consists of 10% salt A and 6% salt b: For producing the chemicals X and Y, the company requires at least 7 gm of Salt A and at least 7 gm of Salt b:If chemical X costs Rs. 10.50 per gm and chemical Y costs Rs. 7.80 per gm, what is the minimum cost at which the company can meet the requirement by using a combination of both types of chemicals?

Let's assume that P gm of chemical X and Q gm of chemical Y to be used to meet the requirement.

So net quantity of salt A in both the chemicals

  A=$$\frac{5}{100}*P$$ + $$\frac{10}{100}*Q \geq 7$$

Similarly net quanity of salt B in both the chemicals 

 B=$$\frac{10}{100}*P$$ + $$\frac{6}{100}*Q \geq 7$$

For minimum cost 

A=$$\frac{5}{100}*P$$ + $$\frac{10}{100}*Q = 7$$

 B=$$\frac{10}{100}*P$$ + $$\frac{6}{100}*Q = 7$$

On solving both equations for P and Q

                            P=40  Q=50

So minimum cost will be = $$40*10.50+50*7.80=810$$