Consider an investment problem where X is the number of shares of a pharmaceutical stock that are purchased and Y is the number of shares of a bank stock that are purchased. The LP has several constraints, but one is a budget constraint that is of the form: 25X + 50Y = 10,000. Thus, a share of X costs $25 and a share of Y costs $50 and a sum of $10,000 is available for investment. Consider the following information from the LP solution:

Optimal value of Objective Function:   $12,500

Optimal value of Decision Variables: X = 128.5; Y= 135.75

Allowed increase in the RHS of Budget Constraint = $1 E + 30

Allowed decrease in the RHS of Budget Constraint = $2,750

Shadow Price of Budget Constraint= $2.50

Answer the following questions considering the information above. The only answers possible for the following questions are "$5,000, "$7,500", "$10,000", "$12,500", "$15,000", or "$17,500":

1) If you discover that you have an additional $2000 to add to the budget constraint, what will be the new value of the Objective Function?  

2) If you decrease the RHS of the budget constraint to $9000, what will be the new value of the Objective Function?

State if the following question is True or False:

3) If the RHS of the Budget Constraint is changed to $7000, the Shadow Price will change to some value other than $2.50. TRUE OR FALSE?