Question

A manufacturing company produces a product from one raw material using a process A.

This process generates total solid wastes WA (in tonne) represented as

WA​(r)=1/15000​(−2r³+10r²+400r) where r is the amount of raw material used in tonne and 

r∈(0,10). If the company uses a different process B to produce the same product from same raw material, then the total solid waste generated is WB (in tonne) represented as W_B(r) = 1/10000(-2.2r³+11r²+440r). The company spends ₹5,000in waste treatment using the process A by consuming 1 tonne of raw material. How much extra amount will the company have to pay in waste treatment for consuming 1 tonne of raw material if it uses the process B?

Answer 1

$$W_A(1)=\dfrac{1}{15000}(-2(1)^3+10(1)^2+400(1))$$

$$=0.0272(tonne)$$

$$W_B(1)=\dfrac{1}{10000}(-2.2(1)^3+11(1)^2+440(1))$$

$$=0.04488(tonne)$$

$$0.04488-0.0272=0.01768$$

$$\dfrac{0.01768}{0.04488}(5000)=1969.70$$

The company will have to pay extra ₹1969.70 in waste treatment for consuming 1 tonne of raw material if it uses the process B.