Consider the linear program in Problem $3.$ The value of the optimal solution is $48.$ Suppose that the right$-$hand side for constraint $1$ is increased from $9$ to $10.$

a$.$ Use the graphical solution procedure to find the new optimal solution.

b$.$ Use the solution to part $($a$)$ to determine the dual value for constraint $1.$

c$.$ The computer solution for the linear program in Problem $3$ provides the following right$-$ hand$-$side range information: