Basic variable Coefficient of XI Right side Z 0)1 (4 16/3-5)/3 /3 11/3 2)02/31/3 0 5/3 5/4, the optimal solution is xI=0, X2=0. X3=5/3 7. The BETTER PRODUCTS COMPANY has decided to initiate the production of four new products, using three plants that currently have excess production capacity The products require a comparable production effort per unit, so the available production capacity of the plants is measured by the number of units of any product that can be produced per day, as given in the following table. The bottom row gives the required production rate per day to meet projected sales. Each plant can produce any of these products, except that plant 2 cannot produce product 3. However, the variable costs per unit of each product differ from plant to plant Management now needs to make a decision on how to split up the production of the products among plants(1 Unit cost for product ty available Plant1 Plant 2 nt 3 Production rate20 Solution: First construct the supply-demand equilibrium table Unit cost for product apacity available 45(D) 75 Plant 2 40 75 Plant 3 37 27 2 000 45 Production rate 20 40 75 Second, solving this problem and get the optimal solution Unit cost for product Capacity available 2 4 5(D) PlantI 4127(3028(30240(15) 75 Plant 2 3(15)0 Plant 3 37(20)302721(25)0 45 Production rate2030 40 The red word in blanks are the optimal shipment, the minimum cost is Z=3260 8. Consider a project whose activities and required times are as given: (10 points Activity Required Time minutes) ,2) (2,3) 55556 Coefficient of : Basic variable Eq. Z X1 X2 X3 X4 X5 Right side Z (0) 1 (14θ -16)/3 (4θ -5)/3 0 0 (7+ θ)/3 X4 (1) 0 5/3 1/3 0 1 -2/3 11/3 X3 (2) 0 2/3 1/3 1 0 1/3 5/3 Whenθ>5/4, the optimal solution is x1=0,x2=0,x3=5/3 7. The BETTER PRODUCTS COMPANY has decided to initiate the production of four new products, using three plants that currently have excess production capacity. The products require a comparable production effort per unit, so the available production capacity of the plants is measured by the number of units of any product that can be produced per day, as given in the following table. The bottom row gives the required production rate per day to meet projected sales. Each plant can produce any of these products, except that plant 2 cannot produce product 3. However, the variable costs per unit of each product differ from plant to plant. Management now needs to make a decision on how to split up the production of the products among plants. (15 points) Unit cost for product 1 2 3 4 Capacity available Plant 1 41 27 28 24 75 Plant 2 40 29 — 23 75 Plant 3 37 30 27 21 45 Production rate 20 30 30 40 Solution: First construct the supply-demand equilibrium table Unit cost for product 1 2 3 4 5(D) Capacity available Plant 1 41 27 28 24 0 75 Plant 2 40 29 — 23 0 75 Plant 3 37 30 27 21 0 45 Production rate 20 30 30 40 75 Second, solving this problem and get the optimal solution Unit cost for product 1 2 3 4 5(D) Capacity available Plant 1 41 27(30) 28(30) 24 0(15) 75 Plant 2 40 29 — 23(15) 0(60) 75 Plant 3 37(20) 30 27 21(25) 0 45 Production rate 20 30 30 40 75 The red word in blanks are the optimal shipment, the minimum cost is Z=3260. 8.Consider a project whose activities and required times are as given: (10 points) Activity Required Time (Minutes) (1,2) (2,3) (3,4) (4,5) 5 5 5 5