Using linear programming model (graphical method).  PROBLEM: Brian, who is currently hospitalized, was prescribed to take vitamin supplements to improve his immunity. Each day, he must take at least 16 units of Energy X, at least 5 units of Energy Y, and at least 20 units of Energy Z. He can choose either tablets or capsules. Each tablet contains 8 units of Energy X, 1 unit of Energy Y, and 2 units of Energy 7. Meanwhile each capsule contains 2 units of Energy X, 1 unit of Energy Y and 7 units of Energy Z. The cost per tablet is $15, and $30 per capsule. How many tablets and capsules should he buy in order to minimize his cost?

Jesaki Furniture Company has two plants that produce lumber used in manufacturing tables and chairs. In 1 day of operation, plant A can produce the lumber required to manufacture 22 tables and 61 chairs, while plant B can produce the lumber required to manufacture 28 tables and 51 chairs. In this production run, the company needs enough lumber to manufacture at least 440 tables and 830 chairs. It costs $875 per day to operate plant A and $850 per day to operate plant B. The company needs to produce sufficient lumber at a minimum cost. This can be set up as a linear programming problem where you minimize the operational cost C. Introduce the decision variables: X=number of days to use plant A Y=number of days to use plant B Find the objective function C

A division of the Winston Furniture Company manufactures dining tables and chairs. Each table requires 40 board feet of wood and 5 labor-hours. Each chair requires 16 board feet of wood and 4 labor-hours. The profit for each table is $45, and the profit for each chair is $20. In a certain week, the company has 3200 board feet of wood available and 520 labor-hours availabl How many tables and chairs should Winston manufacture to maximize its profit? tables chairs What is the maximum profit? $

Ruff, Inc. makes dog food out of chicken and grain. Chicken has 10 grams of protein and 5 grams of fat per ounce, and grain has 2 grams of protein and 2 grams of fat per ounce. A bag of dog food must contain at least 238 grams of protein and at least 158 grams of fat. If chicken costs 9¢ per ounce and grain costs 1¢ per ounce, how many ounces of each should Ruff use in each bag of dog food to minimize cost?  grain ___oz chicken ____oz

A zookeeper has a walrus with a nutritional deficiency. She wants to make sure the walrus consumes at least 2700 mg of iron, 2400 mg of vitamin B-1, and 1800 mg of vitamin B-2, One Maxivite pill contains 500 mg of iron, 200 mg of vitamin B-1, and 100 mg of vitamin B-2, and costs $0.05. One Healthovite pill provides 100 mg of iron, 150 mg of vitamin B-1, and 150 mg of vitamin B-2, and costs $0.06. Complete parts (a)-(c) below. (a) What combination of Maxivite and Healthovite pills will meet the walrus's requirement at lowest cost? What is the lowest cost? Set up the linear programming problem. Let m represent the number of Maxivite pils, h represent the number of Healthovite pills, and c represent the total cost in dollars. Minimize c= 0.05m + 0.06h subject to 500m + 100h 2 2700 200m + 150h 2 2400 100m + 150h 2 1800 m20, h 2 0. (Use integers or decimals for any numbers in the expressions. Do not include the $ symbol in your answers.) The best combination of pilts that moets the walrus's…

The Fidget Spinner emporium sells two types of toys.  A and B.  The store owner pays $8 per toy A and $14 per toy B.  When the emporium sells Toy A, it receives a profit of $2, while from Toy B it receives $3 profit per toy.  Fewer than 2000 toys will be sold, and the emporium cannot spend more than $20,000 to buy the toys.  How many units of each type of toy should the emporium buy?

A bakery gets milk from two dairies then blends the milk to get the desired amount of butterfat for use in the company's best selling product. Milk from dairy I costs $2.10 per gallon, and milk from dairy Il costs $0.70 per gallon. The company has at most $140 available for purchasing milk. Dairy I can supply at most 54 gallons of milk averaging 3.8% butterfat and dairy II can supply at most 88 gallons of milk averaging 3.2% butterfat. The blend can contain no more than 100 gallons of milk and should contain the maximum amount of butterfat. (a) Let x be the number of gallons of milk from dairy I and let y be the number of gallons of milk from dairy II. State the objective function. Maximize z= (b) Excluding nonnegativity constraints, how many constraints are needed for this model? (b) How much milk from each dairy should the bakery use? Round your answers to the nearest integer as needed. gallons from dairy I and gallons from dairy II. (c) What is the maximum amount of butterfat? Round…

The following are recipes for pancakes and waffles. A batch of pancakes require 3 cups of flour, 1 cup of milk, and 2 eggs and feeds 6 people. A batch of waffles requires 2 cups of flour, 2 cups of milk, and 2 eggs and feeds 5 people. Suppose you have available 24 cups of flour, 18 cups of milk, and 20 eggs. How many batches of pancakes and waffles should you make to feed the maximum number of people? a) State what you assign to x and y. Write the objective function. [2] b) Write the three constraint inequalities. [3] c) Find the axes intercepts of each of the above inequalities. [3] d) Plot the inequalities. Label the solution set. [3] e) How many batches of pancakes and waffles should you make to feed the maximum number of people