Where and are the pollution levels from the two sources, and are expenditure levels on pollution reduction. What is the cheapest way of fixing the total pollution level to 1000?

Math/Physic/Economic/Statistic Problems

(a) Two pollution sources can be cleaned up if money is spent on them according to the functions

 

where and are the pollution levels from the two sources, and are expenditure levels (in £000s) on pollution reduction. What is the cheapest way (minimum cost) of fixing the total pollution level to 1000?

(b) Estimate the change in the minimum cost if the total pollution level is required by law to fall to 950?