The Old English Metal Crafters Company makes brass trays and buckets. The number of trays and

buckets that can be produced daily is constrained by the availability of brass and labor, as reflected in

the following linear programming model:

The final optimal simplex tableau for this model is as follows:

a$.$ Formulate the dual of this model.

b$.$ Define the dual variables and indicate their value.

c$.$ Determine the optimal ranges for and

d$.$ Determine the feasible ranges for $($pounds of brass$)$ and $($labor hours$).$

e$.$ What is the maximum price the company would be willing to pay for additional labor hours, and

how many hours could be purchased at that price?