2. The government of Ruritania' has retained you as a mathematical consultant to optimise a climate change policy. To be clear, in the context of this policy the term \"emissions\" refers exclusively to greenhouse gasses. So far, your review has developed a model and a broad policy whose parameters now need to be tuned. All money figures, lowercase s and f, are measured in millions of Ruritanian guineas. The emissions figure, Eg, is measured in megatons-equivalent of carbon dioxide. "Whose politics and climate policies are markedly different from our own. e t4: a direct tax on polluters (any activity or product that emits greenhouse gasses) e t5: additional income taxation on high-earning taxpayvers e s.: government funding to clean industrial processes at source e s,,: government contribution to an international climate change adaptation fund The international adaptation fund contribution is based on Ruritanian emissions, at a rate of 50 Ruritanian guineas per ton-equivalent of carbon dioxide, and the government expects to receive back from the fund 300 million guineas annually to cover the costs of mitigating climate change. Its net contribution is therefore Se td Sm = 300 + 1000 ex ( ) + 1500e () 1 m P\\~ &00 P | ~3g (1) The Prime Minister believes the public will dislike increases in taxes, and in particular will dislike the specific taxes on pollution more than increasing high-earner taxation. She wants you to minimise the overall taxation burden, with a preference to reduce the direct taxes: K =2t;4ty. (2) Her Chancellor of the Exchequer wants the policy to be cost-neutral: tg+1th = s+ Sm- (3] a. Use the method of Lagrange multipliers with multiple constraints to find the optimum for (ta. ty. Se. 5m).2 Your objective function is Eq. (2), and your constraints are Eqq. (1) and (3). b. Write up to two sentences explaining to what extent this policy reflects the \"polluter pays and \"ability to pay\" principles. Write a sentence explaining whether you think that this policy is justified overall