mathematical economics question, please help solve the questions

1. Assume that there are two sources of pollution into a lake. The local water authority can clean up the discharges and reduce pollution levels from these sources but there are, of course, costs involved. The damage effects of each pollution source are measured on a 'pollution scale'.The lower the pollution level the greater the cost of achieving it, as is shown by the cost schedules for cleaning up the two pollution sources: 2, = 479 26',"5 22 = 600 - 3c?s where Z, and Z; are pollution levels and C1 and C; are expenditure levels (in Ms) on reducing pollution. To secure an acceptable level of water purity in the lake the water authority's objective is to reduce the total pollution level to 1.0% by W- How can it do this? 2. A rm faces the production function .J... o = for. l.) = so[o. tit-\"15 + 0. 41.415] '1'. t: can buy the inputs 1: and L at prices per unit of 5 TL and 2 TL respectively. What combination of L and K should be used to maximize output if its input budget is constrained to 150 TL? 3. A consumer's preferences are represented by the utility function, U(X.V)=X"Y'. Budget constraint is M =P,X+P,.Y. Based on this information; a) Derive the Marshallian demand function. b) Calculate zero degree homogeneity for Marshallian demand for X. c) Derive the Hicksian demand function