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A company produces four juice products in quart containers:…

A company produces four juice products in quart containers: (i) orange juice that sells for $2.80 per quart, (ii)  grapefruit juice that sells for $3.00 per quart, (iii) orange-pineapple juice that sells for $3.10 per quart, and (iv) grapefruit-pineapple juice that sells for $3.40 per quart. The costs and available quantities of the juices needed to make these four products are: (a) orange juice at a cost of $3.60 per gallon and 600 gallons available, (b) grapefruit juice at a cost of $4.80 per gallon and 500 gallons available, and (c) pineapple juice at a cost of $4.20 per gallon and 400 gallons available. [Note: One gallon equals four quarts]. The orange-pineapple product must consist of at least 60% pineapple juice. The grapefruit-pineapple product can consist of no more than 60% pineapple juice. The number of quarts of the orange juice product produced should be equal to the number of quarts of the grapefruit juice product produced. The number of quarts of the orange-pineapple product produced should not differ from the number of quarts of the orange juice product produced by more than 150 quarts. The number of quarts of the grapefruit-pineapple product produced should not differ from the number of quarts of the grapefruit juice product produced by more than 200 quarts. Prepare an LP formulation to determine the production quantities for each of the four products that will maximize profit. (Do not attempt to solve or partially-solve the problem in any way when preparing your formulation).