Directions: Formulate but do not solve each of the following problems as a linear programming problem. Be sure to follow the proper order: variables, objective function, constraints, nonnegativity conditions.

An investment broker wants to invest up to $$20,000.$ She can purchase a type A bond yielding a $10\%$ return and she can purchase a riskier type $B$ bond yielding a $15\%$ return. She wants to invest at least as much in the type A bond as in the type $B$ bond to reduce her risk. The minimum investment for the type A bond is $$5,000,$ and there are only $$8,000$ worth of type B bonds available. How much should the broker invest in each type of bond to maximize her returns?