The optimal tableau of an LP is given below. For context, the problem is a maximization program, the three constraints are of form $$ with

corresponding slacks $s_i$ and decision variables are non$-$negative. The first and second constraint are defined by the availability of resource $1$

and resource $2,$ respectively.

Using the optimal tableau and sensitivity analysis, answer the following questions.

How much would the objective function value increase at the optimum if there was one additional unit of resource $1$ available, assuming that

the optimal basis does not change?

i$.5$

ii$.2$

iii. $10$

iv$.$ This cannot be read directly from the tableau.