M&D Chemicals produces two products that are sold as raw materials to companies that manufacture bath soaps and laundry detergents. Based on an analysis of current inventory levels and potential demand for the coming month, M&Ds management specified that the combined production for products A and B must total at least 350 gallons. Separately, a major customers order for 125 gallons of product A must also be satisfied. Product A requires 2 hours of processing time per gallon, and product B requires 1 hour of processing time per gallon. For the coming month, 600 hours of processing time are available. M&Ds objective is to satisfy these requirements at a minimum total production cost. Production costs are $2 per gallon for product A and $3 per gallon for product B.

Linear program for the M&D Chemicals problem:

Min 2A + 3B

s.t. 1A 125 Demand for product A

1A + 1B 350 Total production

2A + 1B 600 Processing time

A, B 0

What is the minimum total cost?

If the unit production cost for product A is $6, what is the optimal gallons of product A to produce? Then what is the minimum total cost?

If the unit production cost for product B is $5, what is the optimal gallons of product B to produce? What is the minimum total cost?

If the demand for product A is 350, what is the minimum total cost?

If the combined production for products A and B must total at least 400, what the minimum total cost?

If 650 hours of processing time are available, what the minimum total cost?

\begin{tabular}{|c|c|c|c|c|c|c|c|} \hline 4 & A & C & D & E & F & G & H \\ \hline 4 & & & & & & & \\ \hline s & \multirow{2}{*}{\multicolumn{7}{|c|}{ Variable Cells }} \\ \hline 6 & & & & & & & \\ \hline 78 & Cell & Name & FinalValux & ReducedCost & ObjectiveCocficient & AllowableIncrease & AllewableDecrease \\ \hline 9 & $$14 & Gallons Produced Product A & 250 & & 2 & 1 & 1E+30 \\ \hline 10 & 3cs14 & Gallons Produced Product B & 100 & 0 & 3 & 1E+30 & 1 \\ \hline 11 & & & & & & & \\ \hline 12 & \multicolumn{7}{|l|}{ Constraints } \\ \hline 1314 & Cell & Name & FinalValue & ShadowPrice & ConstraintR.H.Side & AllowableInerease & AllowableDecrease \\ \hline 15 & $B$19 & Product A Provided & 250 & 0 & 125 & 125 & 1E+30 \\ \hline 16 & $8520 & Tctal Prodoction Provided & 350 & 4 & 350 & 125 & 50 \\ \hline 17 & $B$23 & Frocessing Time Hours Used & 600 & -1 & 600 & 100 & 125 \\ \hline \end{tabular}