Activity #1 Four products are processed sequentially on three machines. The following table gives the data of the problem. Formulate the LP model of the problem. Capacity (hr) 500 Manufacturing time (min) per unit Machine Cost per hour ($) Product 1 Product 2 Product 3 Product4 1 10 2 3 4 2 2 5 3 2 1 2 3 4 7 3 1 1 Unit selling price ($) 75 70 55 45 380 450 Activity #2 All-Natural Coop makes three breakfast cereals, A, B, and C, from four ingredients: rolled oats, raisins, shredded coconuts, and slivered almonds. The daily availabilities of the ingredients are 5 tons, 2 tons, 1 ton, and 1 ton, respectively. The corresponding costs per ton are $100, $120, $110, and $200. Cereal A is 50:5:2 mix of oat raisins and almond. Cereal B is a 60:2:3 mix of oats, coconut, and almond. Cereal C is a 60:3:4:2 mix of oats, raisins, coconut, and almond. The cereals are produced in jumbo 5-lb sizes. All-Natural sells A, B, and C at $2, $2.50, $3.00 per box, respectively. The minimum daily demand for cereals A, B, and C is 500, 600, and 500 boxes, respectively. Develop an LP model to determine the optimal production mix of the cereals and the associated amounts of ingredients. Activity #3 The demand for an item over the next four quarters is 270, 380, 420 and 310 units, respectively. The price per unit starts at $20 in the first quarter and increases by $3 each quarter thereafter. The supplier can provide no more than 480 units in any one quarter. Although we can take advantage of lower process in early quarters. A storage cost of $2.45 is incurred per unit per quarter. In addition, the number of units that can be held over from one quarter to the next must be 95 or less. Develop LP model to find optimum schedule for purchasing the item to meet the demand