Problem 5: Candy Production Blending Problems (20 points, 6, 6, 8 Points) Willy Wonka's Candy Company Produces three types of Candy 1. Wonka Bars 2. Bottle Caps 3. Giant Sweet Tarts In order to produce the different type of candies, Willy can run three different production processes as described below. Each process involves blending different types of sugars in the Magical Factories Mixer. Process 1: Running Process 1 for one hour: Costs: $5 Requires: Two barrels of sugar type A and three barrels of sugar type B Output: Two Wonka Bars and one packet of Bottle Caps Process 2: Running Process 2 for one hour: Costs: $4 Requires: One barrel of sugar type A and three barrels of sugar type B Output: Three packets of Bottle Caps Process 3: Running Process 1 for one hour: Costs: $1 Requires: Two barrels of sugar type B and three packets of Bottle Caps Output: Two Wonka Bars and one packet of Giant Sweet Tarts Incidentally, the barrels are really tiny, and the candy is very sweet. Each week we can purchase: 200 barrels of sugar type A at $2 Per Barrel 1300 barrels of sugar type B at $3 Per Barrel Assume that they can sell everything that they can produce. I Wonka Bars are sold at $9 per bar. Bottle Caps are sold at $10 per packet. I Giant Sweet Tarts are sold at $24 per packet. Assume that 100 hours of mixing time are available. Part A: Formulate an LP whose solution will maximize Willy Wonka's Profits. Part B: Assume that instead of having 200 barrels of sugar type A and 300 barrels of sugar type B available that you can order a total of 500 Barrels. Show how to modify your LP formulation in Part A to account for this revised problem. Part C: Suppose that instead of selling the three candies separately, they can only be sold as part of a box consisting of one Wonka Bar, two packets of Bottle Caps, and one pack of Giant Sweet Tarts. Each Wonka Box sells for $54. Modify your LP formulation in part A to model this new scenario