(15 points) Suppose that the consumer's preferences are given by U (c, !) = 2c3 + 213 where c is the level of consumption and ( is leisure. The consumer has to allocate 24 hours between leisure and labour. The real wage rate is 510 per hour and the real non-wage income is $1520, Assume that there is no (a) Write the budget constraint of the household. (b) Solve for the tangency condition using the marginal rate of substitut tion MRS. ., and the wage (c) Solve for optimal consumption, leisure, and hours worked