Three alloys are made using three different metals in the proportions shown in the following table. The profits earned from the sales of the alloys, and the amounts of available metals are also shown in the table. (a) Formulate an LP to solve the problem of maximizing the profits with the available amounts of metals. Solve the LP. (b) Formulate the dual of the above LP and solve the dual as well. (c) The table also lists the cost ($/kg) for additional amounts of the metals that can be purchased. Without solving any other LP, and using dual optimal solution if necessary, determine the amounts of additional metals that should be purchased to maximize the net profit. (Hint: you'll need to consider perturbations of the amounts of available metals, and use shadow prices.) Three alloys are made using three different metals in the proportions shown in the following table. The profits earned from the sales of the alloys, and the amounts of available metals are also shown in the table. (a) Formulate an LP to solve the problem of maximizing the profits with the available amounts of metals. Solve the LP. (b) Formulate the dual of the above LP and solve the dual as well. (c) The table also lists the cost ($/kg) for additional amounts of the metals that can be purchased. Without solving any other LP, and using dual optimal solution if necessary, determine the amounts of additional metals that should be purchased to maximize the net profit. (Hint: you'll need to consider perturbations of the amounts of available metals, and use shadow prices.)