Hi, I have updated the wuestion with an example of a similar question with solution. I hope this will help.

2 The company TBW produces a number different products. In order to do that they use different materials. The amount of each material needed for each unit of product and each materials availability is given in the table below. Materials Demand Products Z Y X U V Low High Cost A 14 8 13 10 16 18 B 5 8 7 12 5 14 11 2. 37 31 31 29 C 7 11 10 9 14 41 30 3 D 14 7 9 7 13 4 Availability 344 253 288 276 236 The demand of each product is also given in the table above. Since TBW is contracted to produce a certain amount of some products there is a lower bound different from zero as well as an upper bound for some of the products. There is a cost related to producing of each unit of each product. TBW wants to minimize the total cost of production. Construct a model that minimizes the total cost of production respecting the upper and lower bounds of the amount to produce of each product. Also make sure to not use more of any materials than the availability. 4 Given a set of different foods, their nutrient information and price per portion, construct a model that minimize the cost per portion while at the same time meets the daily intake of the different nutrients. Nutrient per unit Food type Calories Fal Fibre Iron Cost per unit Oranges 61.6 0.2 0.1 0.15 Tofu 882 5.5 1.4 6.2 0.31 Couscous 100.8 0.1 1.3 03 0.39 Frozen broccoli 73.8 0.8 8.5 23 0.16 min 2000 0 10 Nutrient demand 25 100 max 2290 65 (6p) Solution: Let Fbe the set of different foods, N be the set of different nutrients, or the cost for one unit of food type f, 4and , be lower and upper limits for each nutrient demand and 24,n the content of nutrient n in food type f. Let x, be the number of units of food type f we use. since we want to minimize the cost our objective function is minimize FX , TET The constraint is that we need to meet the lower and upper bounds for the nutrient content in our food nr,nrum VnEN TET We also have that we can't use a negative amount of food oxy for all food types feF. The final model is minimize X crk TE! subject to . , , TET WEN VET 2 The company TBW produces a number different products. In order to do that they use different materials. The amount of each material needed for each unit of product and each materials availability is given in the table below. Materials Demand Products Z Y X U V Low High Cost A 14 8 13 10 16 18 B 5 8 7 12 5 14 11 2. 37 31 31 29 C 7 11 10 9 14 41 30 3 D 14 7 9 7 13 4 Availability 344 253 288 276 236 The demand of each product is also given in the table above. Since TBW is contracted to produce a certain amount of some products there is a lower bound different from zero as well as an upper bound for some of the products. There is a cost related to producing of each unit of each product. TBW wants to minimize the total cost of production. Construct a model that minimizes the total cost of production respecting the upper and lower bounds of the amount to produce of each product. Also make sure to not use more of any materials than the availability. 4 Given a set of different foods, their nutrient information and price per portion, construct a model that minimize the cost per portion while at the same time meets the daily intake of the different nutrients. Nutrient per unit Food type Calories Fal Fibre Iron Cost per unit Oranges 61.6 0.2 0.1 0.15 Tofu 882 5.5 1.4 6.2 0.31 Couscous 100.8 0.1 1.3 03 0.39 Frozen broccoli 73.8 0.8 8.5 23 0.16 min 2000 0 10 Nutrient demand 25 100 max 2290 65 (6p) Solution: Let Fbe the set of different foods, N be the set of different nutrients, or the cost for one unit of food type f, 4and , be lower and upper limits for each nutrient demand and 24,n the content of nutrient n in food type f. Let x, be the number of units of food type f we use. since we want to minimize the cost our objective function is minimize FX , TET The constraint is that we need to meet the lower and upper bounds for the nutrient content in our food nr,nrum VnEN TET We also have that we can't use a negative amount of food oxy for all food types feF. The final model is minimize X crk TE! subject to . , , TET WEN VET