A farmer uses two types of fertilizers. A 50-lb bag of Fertilizer A contains 8 lb of nitrogen, 2 lb of phosphorus, and 4 lb of potassium. A 50-lb bag of Fertilizer B contains 5 lb each of nitrogen, phosphorus, and potassium. The minimum requirements for a field are 440 lb of nitrogen, 260 lb of phosphorus, and 360 lb of potassium. If a 50-lb bag of Fertilizer A costs $80 and a 50-lb bag of Fertilizer B costs $70, find the amount of each type of fertilizer the farmer should use to minimize his cost while still meeting the minimum requirements. Fertilizer A Fertilizer 8 What is the minimum cost? $ .2.022. bags bags MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER

An animal food must provide 60 units of vitamins and 67 calories per serving. One gram of soybean meal provides 2.5 units of vitamins and 5 calories. One gram of meat byproducts provides 4.5 units of vitamins and 3 calories. One gram of grain provides 5 units of vitamins and 10 calories. A gram of soybean meal costs 7¢, a gram of meat byproducts 9¢, and a gram of grain 10¢. (a) What mixture of these three ingredients will provide the required vitamins and calories at minimum cost? (b) What is the minimum cost? (a) Set up the initial tableau for the dual maximum problem. Fill in the missing entries. X2 S1 S2 S3 2.5 1 4.5 3 10 10

A farmer uses two types of fertilizers. A 50-lb bag of Fertilizer A contains 8 lb of nitrogen, 2 lb of phosphorus, and 4 lb of potassium. A 50-lb bag of Fertilizer B contains 5 lb each of nitrogen, phosphorus, and potassium. The minimum requirements for a field are 440 lb of nitrogen, 260 lb of phosphorus, and 360 lb of potassium. If a 50-lb bag of Fertilizer A costs $80 and a 50-lb bag of Fertilizer B costs $70, find the amount of each type of fertilizer the farmer should use to minimize his cost while still meeting the minimum requirements. Fertilizer A      bags Fertilizer B      bags What is the minimum cost? $

The Sanders Garden Shop mixes two types of grass seed into a blend. Each type of grass has been rated (per pound) according to its shade tolerance, ability to stand up to traffic, and drought resistance, as shown in the table. Type A seed costs $1 and Type B seed costs $2. If the blend needs to score at least 300 points for shade tolerance, 400 points for traffic resistance, and 750 points for drought resistance, how many pounds of each seed should be in the blend? Which targets will be exceeded? How much will the blend cost?   Type A Type B Shade Tolerance 1 1 Traffic Resistance 2 1 Drought Resistance 2 5

A zookeeper has a walrus with a nutritional deficiency. She wants to make sure the walrus consumes at least 2300 mg of iron, 2700 mg of vitamin B-1, and 1200 mg of vitamin B-2. One Maxivite pill contains 300 mg of iron, 300 mg of vitamin B-1, and 50 mg of vitamin B-2, and costs $0.06. One Healthovite pill provides 100 mg of iron, 150 mg of vitamin B-1, and 150 mg of vitamin B-2, and costs $0.04. 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 pills, h represent the number of Healthovite pills, and c represent the total cost in dollars. C= subject to 300m + 100h 300m + 150h 50m + 150h m20, h 2 0. (Use integers or decimals for any numbers in the expressions. Do not include the $ symbol in your answers.)

Departments X, Y, and Z occupy floor space of 80m2, 140m2 and 160m2respectively. If the total rental costs for floor space is $11400 per month, how much of the rental cost should each department pay?

Bibbins Manufacturing produces softball and baseballs for youth recreation leagues. Each softball costs $11 to produce and sells for $17 while each baseball costs $10.50 and sells for $15. The material and labor required to produce each item is listed here along with the availability of each resource. Amount Required Per Amount Resource Softball Baseball Available Leather 5 oz 4 oz 6,000 oz Nylon 6 yds 3 yds 5,400 yds Core 4 oz 2 oz 4,000 oz Labor 2.5 min 2 min 3,500 min Stitching 1 min 1 min 1,500 min If X, = number of softballs to produce, X, = number of baseballs to produce, what is the objective function? МАХ 6 X, +4.5 X2 MIN 6X, + 4 X2 МАX 11 X, + 17 X2 МAX 2.5 X, + 6 X2

A farmer can buy two types of plant food, mix A and mix B. Each cubic yard of mix A contains 36 pounds of phosphoric acid, 27 pounds of nitrogen, and 9 pounds of potash. Each cubic yard of mix B contains 12 pounds of phosphoric acid, 27 pounds of nitrogen, and 24 pounds of potash. The minimum monthly requirements are 540 pounds of phosphoric acid, 810 pounds of nitrogen, and 360 pounds of potash. Find the set of feasible solutions graphically for the amounts of mix A and Ay 50- 40- mix B that can be used. 30- If x is the number of cubic yards of mix A used and y is the number of cubic yards of mix B used, write a system of linear inequalities that indicates appropriate restraints on x and y. Write an inequality for the constraint on phosphoric acid. Complete the inequality below. 20- 540 10- 10 20 30 40 30

A farmer can buy two types of plant food, mix A and mix B. Each cubic yard of mix A contains 20 pounds of phosphoric acid, 30 pounds of nitrogen, and 5 pounds of potash. Each cubic yard of mix B contains 10 pounds of phosphoric acid, 30 pounds of nitrogen, and 10 pounds of potash. The minimum monthly requirements are 430 pounds of phosphoric acid, 990 pounds of nitrogen, and 210 pounds of potash. If mix A costs $20 per cubic yard and mix B costs $35 per cubic yard, how many cubic yards of each mix should the farmer blend to meet the minimum monthly requirements at a minimum cost? What is this cost? If mix A costs $20 per cubic yard and mix B costs $35 per cubic yard, the farmer should blend yd³ of mix A and requirements at a minimum cost. yd³ of mix B to meet the minimum monthly The cost is $

Cully Furniture buys two products for resale: big shelves (B)and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75,000 to invest in shelves this week, and the warehouse has 18,000 cubic feet available for storage. Profit for each big shelf is $300 and for each medium shelf is $150. Which of the following is not a feasible purchase combination? Group of answer choices 100 big shelves and 82 medium shelves 150 big shelves and 0 medium shelves 100 big shelves and 100 medium shelves 100 big shelves and 0 medium shelves