Exam 17: Linear Programming

In a linear programming problem,multiple optimal solutions are possible if _____.

A firm produces shaving cream and razor.The profit contribution of shaving cream is $2 per unit and that of razor is $4 per unit.The firm wishes to maximize total profit under certain constraints.What would be the slope (-razor/shaving cream,where represents the change in the variables)of the firm's objective function?

A firm produces tires by utilizing machine-hours and labor-hours.It has the choice of producing through three separate processes using different combinations of inputs.The optimization can be done by undertaking a process singly or in combination.The combination matrix is provided below: Process 1(X₁)Process 2(X₂)Process 3(X₃) Machine-hours 1 2 3 Labor-hours 3 2 1 The firm can rent a machine at a price $10 and hire a labor at a wage $15.The firm needs to produce a minimum target of 50 tires per day. (a)Formulate and solve a linear programming problem which will minimize the firm's daily cost (C).

The shadow price of a nonbinding constraint is _____.

An investor wishes to maximize the return on her portfolio and also maintain certain liquidity and risk standards.The alternatives and their corresponding returns are: Alternative Return Municipal Bonds (M)6.2% Certificates of Deposit (S)5.1% Treasury Bills (T) 6.9% AA Bonds (B)10.5% The investor wishes to have at least 25% of the portfolio in Treasury Bills,no more than 20% in AA bonds;no more than 15% in Certificates of Deposit,and no more than 10% in municipal bonds.Formulate a linear programming problem for the investor seeking to maximize the expected return of a $200,000 portfolio.