3. A manufacturer must produce two products in sufficient quantity to meet contracted sales in each of the next 3 months. The two products share the same production facilities, and each unit of both products requires the same amount of production capacity. The available production and storage facilities are changing month by month. so the production capacities, unit production costs, and unit storage costs vary by month. Therefore, it may be worthwhile to overproduce one or both products in some months and to store them until needed For each month, the second column of the following table gives the maximum number of units of the two products combined that can be produced on regular time (RT) and on overtime (OT). For each product, the subsequent columns give (1)the number of units needed for the contracted sales, 2)the cost per unit produced on regular time, (3)the cost per unit produced on overtime, and(4) the cost of storing each extra unit that is held over into the next month In each case. the numbers for the two products are separated by a slash, with the number for ProductI on the left and the number for product 2 on the right Maximum Combined Production Product 1/ Product 2 Production Unit cost Month RT OT esRT ot of storage 10 5/315/16 18/20 1/2 3/517/520/8 2/1 10 The production manager wants a schedule developed for the number of units of each product to be produced on regular time and (if regular time production capacity is used up)on overtime in each of the three months. The objective is to minimize the total of the production and storage costs while meeting the contracted sales for each month. There is no initial inventory and no final inventory is desired after 3 months Formulate this problem as a transportation problem by constructing the appropriate cost and requirements table. (10 points 4. Consider the following problem Maxz=4x,+5x2+3x3 x,+2x,≥2( x3 0 2-5x3≤50 +3x2+5x3 x1≥0,x2≥0,x3≥0 Use the simplex method to demonstrate that this problem does not posses any feasible solutions(15 points) 5. Consider the following problem. (10 points)2 3.A manufacturer must produce two products in sufficient quantity to meet contracted sales in each of the next 3 months. The two products share the same production facilities, and each unit of both products requires the same amount of production capacity. The available production and storage facilities are changing month by month, so the production capacities, unit production costs, and unit storage costs vary by month. Therefore, it may be worthwhile to overproduce one or both products in some months and to store them until needed. For each month, the second column of the following table gives the maximum number of units of the two products combined that can be produced on regular time (RT) and on overtime (OT). For each product, the subsequent columns give (1) the number of units needed for the contracted sales, 2) the cost per unit produced on regular time, (3) the cost per unit produced on overtime, and (4) the cost of storing each extra unit that is held over into the next month. In each case, the numbers for the two products are separated by a slash, with the number for Product1 on the left and the number for Product 2 on the right. Maximum Combined Production Product 1/ Product 2 Unit Cost of Production Month RT OT Sales RT OT Unit cost of storage 1 2 3 10 8 10 3 2 3 5/3 3/5 4/4 15/16 17/15 19/17 18/20 20/18 22/22 1/2 2/1 The production manager wants a schedule developed for the number of units of each product to be produced on regular time and (if regular time production capacity is used up) on overtime in each of the three months. The objective is to minimize the total of the production and storage costs while meeting the contracted sales for each month. There is no initial inventory, and no final inventory is desired after 3 months. Formulate this problem as a transportation problem by constructing the appropriate cost and requirements table. (10 points) 4. Consider the following problem ⎪ ⎪ ⎩ ⎪ ⎪ ⎨ ⎧ ≥ ≥ ≥ + + ≤ + − ≤ + + ≥ = + + 0, 0, 0 3 5 30 15 6 5 50 2 20 . . 4 5 3 1 2 3 1 2 3 1 2 3 1 2 3 1 2 3 x x x x x x x x x x x x st MaxZ x x x Use the simplex method to demonstrate that this problem does not posses any feasible solutions. (15 points) 5.Consider the following problem. (10 points)