2. [Application: Labor supply),r and fertility problem] Consider a consumer's decision problem in having to allocate her time between working, leisure and having children. This individual is endowed with T units of time which she can divide between working (h), her own leisure (l) and children. The hourly wage rate is w; therefore, if she works h. hours, her labor income is 10h. Additionally, she also receives an allowance I from her wealthy father. She uses this total income to purchase a good 3.: for her own consumption which is priced at 3) per unit. Having and rearing each child requires a time commitment of t, plus c units of the consumption good. Assume that her preferences over her own consumption r, her own leisure l, and children in, are given by the following utility function: Mam) =10g(-\\/E + x/E + tax/E). (i) write the consumer's optimization problem with the appropriate re source constraints, and derive the amount of labour she supplies in the market. (ii) \"Then may this individual decide not to work at all