Three polymers are available with the composition shown belo

Three polymers are available, with the composition shown below. It is desired to form a polymer blend that contains 30% of (CH4)x, 30% of (C2H6)x, and 40% of (C3H8)x.

A) Determine the percentages of compounds A, B, and C to achieve the target blend.

B) A new polymer, D, is available. It contains 10% of (CH₄)_x, 30% of (C₂H₆)_x, and 60% of (C₃H₈)_x. Can you blend A, B, C, and D to achieve the target blend?

Solution

A) Let amount of compound A, B and C needed be a, b and c respectively to form 1 unit of blend product, then we can write following equations

(CH₄)_x : 0.25a + 0.35b + 0.55c = 0.3

(C₂H₆)_x: 0.35a + 0.20b + 0.40c = 0.3

(C₃H₈)_x: 0.40a + 0.45b + 0.5c = 0.4

Solving these simultaneous equations we get

a = 0.6, b= 0.35 and c=0.05

Percentages of compounds A,B and C are 60%, 35% and 5% respectively.

B) Let amount of compound A, B, C and D needed be a, b, c and d respectively to form 1 unit of blend product, then we can write following equations

(CH₄)_x : 0.25a + 0.35b + 0.55c + 0.1d= 0.3

(C₂H₆)_x: 0.35a + 0.20b + 0.40c + 0.3d= 0.3

(C₃H₈)_x: 0.40a + 0.45b + 0.5c + 0.6d= 0.4

Clearly we can see that number of variable is 1 more than the number of equations.Therefore, we can have multiple solutions for this system of equations.

So, we can blend A, B, C and D in ultiple ways to get the desired product.