Question

A financial advisor has up to 50,000$ to invest, with the stipulation that at least $15000 is used to purchase Treasury bonds and at most $25,000 in corporate bonds. a) Construct a set of inequalities that describes the relationship between buying corporate vs Treasury bonds, where the total amount invested must be less than or equal to $30,000. ( Let C be the amount of money invested in corporate bonds, and T the amount invested in Treasury bonds) b) construct a feasible region of investment; that is, shade in the area on a graph that satisfies the spending constraints on both corporate and treasury bonds.

Answer 1

a). Let C be the amount of money invested in Corporate bonds, and T the amount invested in Treasury bonds. Since the financial advisor has up to $ 50,000 to invest, hence C+T ≤ 50000…(1).

Also, since at least $15000 is to be used to purchase Treasury bonds, hence T ≥ 15000…(2).

Further, as at most $25,000 is to be invested in the Corporate bonds, hence C ≤ 25000…(3).

b). A graph of the lines C+T = 50000 ( in red) , T = 15000 ( in blue) and C = 25000 ( in green) is attached. The feasible region is on or below the red line, on and above the blue line and on and to the left of the green line in the 1^st quadrant ( as C ≥ 0 and T ≥ 0).

A graph of the shaded feasible area ABCD is attached.