With the rising cost of gasoline and increasing prices to consumers, the use of additives to enhance performance of gasoline may be considered. Suppose there are two additives, Additive 1 and Additive 2, and several restrictions must hold for their use: First, the quantity of Additive 2 plus twice the quantity of Additive 1 must be at least 1=2 lb per car. Second, 1 lb of Additive 1 will add 10 octane units per tank, and 1 lb of Additive 2 will add 20 octane units per tank. The total number of octane units added must not be less than 6. Third, additives are expensive and cost $1.53 per pound for Additive 1 and $4.00 per pound for Additive 2.

a. Build a linear programming model and determine the quantity of each additive that meets the restrictions and minimizes their cost.

b. Perform a sensitivity analysis on the cost coefficients and the resource values. Prepare a letter discussing your conclusions from your sensitivity analysis.