Problems A farmer uses two types of fertilizers. A 75-lb. bag of Fertilizer A contains 10 lbs. of potassium, 2 lbs. of phosphorus, and 6 lbs. of nitrogen. A 75-lb. bag of Fertilizer B contains 5 lbs. each of potassium, phosphorus, and nitrogen. The minimum requirements for a field are 420 lbs. of potassium, 240 lbs. of phosphorus, and 360 lbs. of nitrogen. If a 75-lb. bag of Fertilizer A costs $35 and a 75-lb. bag of Fertilizer B costs $25, find the amount of each fertilizer the farmer should use to minimize her cost while still meeting the minimum requirements. What is the cost? What are the extra resources? Part 1 of 3 Part 1: Set up the linear programming problem. (a.) Define the variables. {x = 1 pounds of Fertilizer A used (x = number of Fertilizer A bags used = Fertilizer A {x = Fertilizer B (x = cost of Fertilizer A (in dollars) {x = cost of Fertilizer B (in dollars) (b.) State the objective. The objective is to minimize ✔ minimize cost✔ cost. (c.) Write the objective function. C = 35x+25y (d.) Write the constraints. 35x + 25y 10x+5y420 2x+5y240 42010x+5.. (potassium requirement) Y 2402x+5y (phosphorus requirement) 6x+5y360 3606 +5. y (nitrogen requirement) x≥ 0, y≥ 0 Part 2 of 3 Part 2: Solve using the appropriate simplex method. Show work by switching to a maximum LP problem, creating the initial simplex tableau, circling the first pivot element, and giving the final simplex tableau. (e.) Switch to a maximization LP problem. Maximize P = -C = -35x-25y (f.) Set up the initial simplex tableau. x y u V W P Constants -10 -5 1 0 0 -420 -2 -5 0 0 0 -240 -6 -5 0 1 0 -360 35 25 ✔ 0 0 0 1 0 (g.) Give the location of the first pivot. Row: Row 1 Column: Column 1 (h.) Give the final simplex tableau. < x y u v W P Constants 1 0 -1 0 -1 × 0 42 0 |1 -1 0 -1 × 0 0 ☑ 0 0 1 1 -1 × 0 10 ☑ 0 10 -1 0 -1 × 1 0

Animal feed is to be made from corn and mixed seeds. One pound of corn has 30 units of fat and 20 units of protein. One pound of mixed seeds has 20 units of fat and 40 units of protein. The feed must supply a daily requirement of 2800 units of fat and 2200 units of protein. What combination of corn and mixed seeds should be used in or- der to make a feed that has a mini- mum total weight? Mixture of corn and other seeds.

A farmer has 165 acres of land suitable for cultivating crops A and B. He has enough seeds available to plant 110 acres of crop A and 115 acres of crop B. Each acre of crop A requires 18 hours of labor, and each acre of crop B requires 19 hours of labor. The farmer has at most 3420 hours of labor available. He expects to make a profit of 130 dollars per acre on crop A and 190 dollars per acre on crop B. How many acres should the farmer plant in order to maximize his profit? acres of crop A, and acres of crop B.

an artist makes three types of ceramic statues( large, medium and small) at monthly cost of $880 for 250 statues. the manufacturing costs for the three types are $5,$4,$3. if the statues sell for $26, $18, and $15, respectively, how many of each type should be made to produce $4,240 in monthly revenue Large ? Medium ? Small ?

A patient takes vitamin pills. Each day he must have at least 1080 IU of vitamin A, 16 mg of vitamin B₁, and 200 mg of vitamin C. He can choose between pill 1, which contains 150 IU of vitamin A, 2 mg of vitamin B₁, and 20 mg of vitamin C, and pill 2, which contains 120 IU of vitamin A, 2 mg of vitamin B₁, and 40 mg of vitamin C. Pill 1 costs 15¢, and pill 2 costs 45¢. Complete parts a and b below. a. How many of each pill should he buy in order to minimize his cost? What is the minimum cost? He should buy of pill 1 and of pill 2. The minimum cost is $

Assume that each gallon of Deluxe Vanilla uses 2 quarts of milk, 2 quarts of cream, and 3 ounces of vanilla; each gallon of Regular Vanilla uses 3 quarts of milk, 1 quart(s) of cream, and 1 ounces of vanilla; and each gallon of Deluxe Chocolate uses 2.75 quarts of milk, 1.25 quarts of cream, and 5 ounces of cacao. Assume also that the shop has on hand 115 gallons of milk, 77 gallons of cream, 19 pounds of vanilla, and 25 pounds of cacao. How many gallons of each type of ice cream should the shop make to use up all of these ingredients? When you setup a system of linear equations to solve this problem, how many variables and how many equations should you have.?Number of variables:    Number of equations:

A company produces coffee makers. The labor cost of assembling one coffee maker during the regular business hours is $2.85. If the work is done in overtime, the labor cost is $3.85 per unit. The company must produce 820 coffee makers this week, and does not want to spend more than $2557 in labor costs. What is the smallest number of units that must be assembled during the regular hours?

Bevco manufactures an orange flavored soft drink called Oranj by combining orange soda and orange juice. Each ounce of orange soda contains 0.5 oz of sugar and 1 mg of vitamin   Each ounce of orange juice contains 0.25 oz of sugar and 3 mg of vitamin C. It costs Bevco 2¢ to produce an ounce of orange soda and 3¢ to produce an ounce of orange juice. Marketing department has decided that each 10 oz bottle of Oranj must contain at least 20 mg of vitamin C and at most 4 oz of sugar. Use LP to determine how Bevco can meet marketing dept.’s requirements at minimum cost.