Cost minimization A plastic polymer requires two chemical additives, alpha and beta, in order to have dimensional stability, be able to withstand a specified amount of punching shear, and to have the required amount of tensile strength. After some experimentation, the manufac- turer determined that the following relationships will satisfy the desired characteristics for each 100 kilograms of polymer:

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3 alpha2 beta > 900 grams 1 alpha + 2 beta > 500 grams REQUIRED 1.4 alpha +1.7 beta > 595 grams Within the above constraints, the decision is to use the most economical combination of the two chemicals, given their cost of $4 per gram each. a. Diagram the solution to the above linear programming problem. b. Determine the optimal combination of additives. c. Determine the optimal combination if the price of beta increases to $6 per gram.