Cola Company blends two different types of soda (regular and MAX Cola) from three refining streams (1, 2, and 3). The streams operate at fixed capacities of 9,000, 7,000, and 5,000 gallons per week. The soda types are sold at prices of $1.00 and $1.20 per gallon, respectively, and any output of the three streams not used in the production of either soda is sold at prices of $.30, $.35, and $.40, per gallon respectively. At least 4,000 gallons of regular soda must be produced per week to satisfy a contract. The minimum calorie count numbers are 80 on regular and 90 on MAX. Assume that each stream contributes to the calorie number an amount equal to the product of its octane number and its fraction of the total volume of the mixture. The calorie ratings of the three streams are 75, 85, and 95.
Assuming the company wants to maximize revenues, develop the LP model that will indicate the optimum weekly volumes of regular and classic soda to produce.
a. Formulate an LP problem to determine the highest Revenue. Write problem formulation. Be sure to define your variables.
b. Solve the problem and write final answers below.
Optimum Objective Function Value Z = $ ____________
Optimum Solution:
Regular MAX
Stream 1
Stream 2
Stream 3
Byproduct 1
Byproduct 2
Byproduct 3
Attach LP model in Excel