The following information describes a possible negative income tax for a family consisting of two adults and two children. The plan would guarantee the poor a minimum income while encouraging a family...

The following information describes a possible negative income tax for a family consisting of two adults and two children. The plan would guarantee the poor a minimum income while encouraging a family to increase its private income (0 ≤ x ≤ 20,000). (A subsidy is a grant of money.)

Family’s earned income: I = x

Subsidy: S = 10,000 – ½ x

Total income: T = I + S

(a) Write the total income T in terms of x. (b) Use a graphing utility to find the earned income x when the subsidy is $6600. Verify your answer algebraically. (c) Use the graphing utility to find the earned income x when the total income is $13,800. Verify your answer algebraically. (d) Find the subsidy S graphically when the total income is $12,500.