They have determined that, ideally, a household would consume at least 10kg of meat each week. The government has proposed implementing a new voucher scheme to ensure that the 10kg per week consumption target is met. To limit the cost of the voucher scheme, the value of the vouchers sent to a household would be linked to the household's income

Using data from household surveys, you have determined that the 'typical' household's

preferences are represented by the utility function

U= (x+ 36)y

where x represents the quantity of meat consumed, and y represents the quantity of the composite good consumed. The associate marginal utilities are.

MU_x= y and MU_y=x+ 36.

The price of meat is P_x= $12 per kg, and the price of the composite good is normalised to P_y= 1.

the marginal rate of substitution of a typical household is Y / (X + 36).

Find the household's demands for 'fruit and vegetables', and for the composite good, as functions of the household's weekly income I. Hint: There is a critical income level below which the household's optimal consumption basket is a corner solution?