You should submit all your Excel files through D2L. Question 1:
The Kalo Fertilizer Company makes a fertilizer using two chemicals that provide nitrogen, phos¬phate, and potassium. A pound of ingredient 1 contributes 10 ounces of nitrogen and 6 ounces of phosphate, while a pound of ingredient 2 contributes 2 ounces of nitrogen, 6 ounces of phos¬phate, and 1 ounce of potassium. Ingredient 1 costs $3 per pound, and ingredient 2 costs $5 per pound. The company wants to know how many pounds of each chemical ingredient to put into a bag of fertilizer to meet the minimum requirements of 20 ounces of nitrogen, 36 ounces of phos¬phate, and 2 ounces of potassium while minimizing cost.
a. Formulate a linear programming model for this problem.
b. Solve this model by using graphical analysis.
Question 2: Solve the following linear programming model graphically:
maximize Z = 3x1 + 2x2 subject to
2x1 + 4x2 22 -xi + 4x2 .s 10 4x1 -2x2 14
- 3x2 5- 1
X 1 , X 2 0
Question 3: Solve the following linear programming model graphically and explain the solution result:
maximize Z = 110x1 + 75x2 subject to
2x 1 + x2 40
6x1 + 8x2 120
70x, + 105x2 2,100
xi, x2 0
Question 4: The Food Max grocery store sells three brands of milk in half-gallon cartons-its own brand, a local dairy brand, and a national brand. The profit from its own brand is $0.97 per carton, the profit from the local dairy brand is $0.83 per carton, and the profit from the national brand is $0.69 per carton. The total refrigerated shelf space allotted to half-gallon cartons of milk is 36 square feet per week. A half-gallon carton takes up 16 square inches of shelf space. The store manager knows that each week Food Max always sells more of the national brand than of the local dairy brand and its own brand combined and at least three times as much of the national brand as its own brand. In addition, the local dairy can supply only 10 dozen cartons per week. The store manager wants to know how many half-gallon cartons of each brand to stock each week in order to maximize profit.
a. Formulate a linear programming model for this problem.
b. Solve this model by using the computer.
Question 5: a. If Food Max in Problem 4 could increase its shelf space for half-gallon cartons of milk, how much would profit increase per carton?
b. If Food Max could get the local dairy to increase the amount of milk it could supply each week, would it increase profit?
c. Food Max is considering discounting its own brand in order to increase sales. If it were to do so, it would decrease the profit margin for its own brand to $0.86 per carton', but it would cut the demand for the national brand relative to its own brand in half. Discuss whether the store should implement the price discount.
Question 6: Art Kumar lives on the outskirts of Draper and has a I -acre lot next to his home. He plans to grow vegetables on the lot and sell them at the downtown market during the summer. He doesn't have enough time to grow the vegetables himself so he has hired a local college student to plant and tend the garden and sell the crops at the market. Art is considering five vegetables to plant that seem to be popular at the market-asparagus, corn, tomatoes, green beans, and red peppers. Art estimates the following yields per acre for each vegetable-2,000 pounds of asparagus, 7,200 pounds of corn, 25,000 pounds of tomatoes, 3,900 pounds of green beans, and 12,500 pounds of red peppers. The costs per acre are $1,800 for asparagus, $1,740 for corn, $6,000 for tomatoes, $3,000 for green beans, and $2,700 for red peppers. Asparagus sells for $1.90 per pound, corn sells for $0.10 per pound, tomatoes sell for $3.25 per pound, green beans sell for $3.40 per pound, and red peppers sell for $3.45 per pound. He has budgeted $5,000 for the garden. Talking to some of the other market vendors, he estimates that he will not sell more than 1,200 pounds of asparagus, 10,000 pounds of tomatoes, 2,000 pounds of green beans, and 5,000 pounds of red peppers. Art wants to know the portion of his lot that he should plant with each vegetable in order to maximize his revenue.
a. Formulate a linear programming model for this problem
b. Solve the model by using the computer.
01: An agriculture company received an order from a local chicken farmer for 8,000 pounds of feed. The farmer wants this feed to contain at least 20% corn, 15% grain, Feed
1 Feed
2 Feed