Q9 Eric’s utility from drinking hot drinks is represented by:u(c,t)2c2+t2Where c is the number of cups of coffee he drinks in a given week and t is thenumber of cups of tea he drinks.(a)Last week Eric’s utility from drinking hot drinks was equal to 6.Write down anequation that expresses the different combination of drinks that he might havedrunk.Then rearrange this equation into a function,t(c),with c as theindependent variable and t as the dependent variable.(b)How much tea would Eric have drunk last month if he has also drank 0,4,or 9cups of coffee?Explain why the domain of the t(c)function is0≤c≤9.()Differentiate the t(c)function to show that it is a decreasing convex function.(d)Sketch the function.(e)Now consider again the general utility function u(c,t)given at the start of thequestion.Find the partial derivatives and Interpret your results.(Compare Eric’s additional utility from drinking one more cup of coffee todrinking one more cup of tea.(g)Eric is offered the choice between either a cup of tea or a cup of coffee,but can’tdecide which to take because he is indifferent.What can we infer about howmuch tea and coffee he has already drank?