Set up the initial SIMPLEX tableau for the given problem. Then solve it

1. Juice Business: A juice blender has the following amounts of three kinds of juice: 90 gallons of pineapple juice, 80 gallons of orange juice, and 50 gallons of mango juice. To create its signature juice WildSplash, the juice blender uses 2 gallons of pineapple juice, 1 gallon of orange juice, and 1 gallon of mango juice. To create the new mixture TastyTreat, the juice blender uses 1, 2, and 1 gallon, respectively, of each type of juice. If the juice blender sells the mixtures wholesale at the price of $12 for a batch of WildSplash and $10 for a batch of TastyTreat, how many batches of each product should be created to obtain maximum gross income? What is the maximum gross income?

Mathematics with Applications In the Management, Natural and Social Sciences