please help me answer this question. thanks

also please explain the answer and draw any relvant diagram to support

Q6. Assume an individual has a utility function of this form U(C,L) = 12 + 2(CXL) This utility function implies that the individual's marginal utility of leisure is 2C and her marginal utility of consumption is 2L where C and L represent the amount of consumption good and hours of leisure, respectively. The individual has an endowment of V dollars in non- labour income and T = 16 hours to either work (h) or use for leisure (L). Assume also that this individual has to pay 25 % labour earnings tax to the government. a) How much utility does the individual receive if she consumes C = 5 and works h = 7 hours? (4 points) b) Write down and graphically indicate the budget constraint of the individual. Let p=price of consumption good and w=before tax wage rate. (6 points) c) Assume the price of each unit of consumption good p = 15 and the before tax wage rate for each hour of work w = 16, and V = 30 dollars. What is the optimal amount of consumption and leisure? (12 points) d) Assume a cash grant welfare program is instituted which pays M = 45 dollars for individuals who do not work. Compute the new optimal labour supply for this individual under the welfare program. Assume that prior to the welfare program, p = 15, w = 16, and V =30 (as in part c). Does the individual accept the welfare program and not work? Show why or why not. (8 points)