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:
- 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? ($5,000, $7500, $10000, $12500, $15000, or $17500)
- If you decrease the RHS of the budget constraint to $9000, what will be the new value of the Objective Function? ($5,000, $7500, $10000, $12500, $15000, or $17500)
- 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?)