A government introduces a policy to subsidize its civilians in the consumption of a non- discrete good, say y. To avoid some people who may abuse the subsidy, however, the government provides a 70% subsidy on the total expenditure on y only up to the consumption of 4 units per month; any extra consumption beyond 4 units and up to 8 units will only be eligible for a 30% subsidy; and no more subsidy will be provided for any consumption beyond 8 units (i.e. if a consumer wants to consume more than 8 units, s/he has to pay the full price for the extra units). Assume that the market price of x is 10 per unit, and the average price of all other goods in the economy, denoted by y, is 4 per unit. If a consumer has a monthly income of 76 and a utility function of u(x,y) (x + 2) (y + 1). To maximize her utility, (a) how many units of x would the consumer consume? (b) how much does the government have to subsidize the consumer? (c) Illustrate the consumer's choice with a diagram.