(b) A factory makes three types of furniture: A, B, and C. Each furniture requires the services of three sections. The cutting, assembly and packaging sections have available a maximum of 60, 80, and 50 labour-hours per week, respectively. For furniture A, it takes 2 hours in cutting section, 2 hours in assembly and 4 hours in packaging. Meanwhile for fumiture B, it takes 2 hours in cutting section, 3 hours in assembly and 2 hours in packaging. Furniture C takes 3 hours in cutting section, 4 hours in assembly and an hour in packaging. Write the system of linear equations. Hence, determine how much furniture of each type must be produced each week for the factory to operate at full capacity using

A female bodybuilder is designing her diet leading up to a competition. To meet her macronutrient goals, she needs to consume at least 240 grams of protein and at least 30 grams of fat per day. Additionally, she needs to eat at most 120 grams of carbohydrates per day. Her goal is to meetthese goals while minimizing her sodium intake. She plans to eat only three foods: eggs, white rice, and oatmeal. Each serving of eggs has 6 grams of protein, 5 grams of fat, and no carbohydrates. Each serving of white rice has 4 grams of protein, no fat, and 40 grams of carbohydrates. Finally,each serving of oatmeal has 6 grams of protein, 3 grams of fat, and 20 grams of carbohydrates. The eggs, white rice, and oatmeal has 60, 2, and 80 units of sodium respectively. What I Have: (a) Define the decision variables.(b) What is the objective? (c) Give all constraints for this linear programming problem.(d) Give all constraints for this linear programming problem so that all inequalities are in ≤ form.(e)…

A dietician is planning a snack package of fruit and nuts. Each ounce of fruit will supply 1 unit of protein, 2 units of carbohydrates, and 1 unit of fat. Each ounce of nuts will supply 1 unit of protein, 1 unit of carbohydrates, and 1 unit of fat. Every package must provide at least 8 units of protein, at least 12 units of carbohydrates, and no more than 11 units of fat. Let x equal the ounces of fruit and y equal the ounces of nuts to be used in each package. a. Write a system of inequalities to express the conditions of the problem. b. Graph the feasible region of the system. a. Fill in the chart. Protein Carbohydrates Fat Fruit unit(s) per ounce unit(s) per ounce unit(s) per ounce Nuts unit(s) per ounce unit(s) per ounce unit(s) per ounce .. Requirements per package At least At least No more than unit(s) unit(s) unit(s)

A manufacturer of skis makes two types of skis: downhill and cross-country skis. The ski production process involves two steps: manufacturing and finishing. The manufacturing time is 3 hours per ski for downhill skis and 2 hours per ski for cross-country skis. The finishing time is 5 hours per ski for downhill skis and 2 hours per ski for cross-country skis. There are only 20 hours per week available for the manufacturing process and 25 hours for the finishing process. Due to existing sales contracts, at most 3 cross-country skis can be made for each downhill ski. The average profit is $43 for each downhill ski and $52 for cross-country ski. The manufacturer wants to know how many of each type of ski should be made to maximize the weekly profit. (a) Identify and clearly define the variables needed to solve the linear programming problem. x=     y=     P=      (b) Find the objective function. Select whether it's maximizing or minimizing in the first answer blank and enter your…