MAT/540 MAT540 MAT 540 WEEK 6 HOMEWORK

MAT 540 WEEK 6 HOMEWORK

Week 6 Homework 

• Week 6 Homework Template

• MAT540 Homework
• Week
• 6
• Page
• 1
• of
• 2
• MAT5
• 40
• Week
• 6
• Homework
• Chapter 2
• A
• Cereal Company makes a cereal from several ingredients. Two of the ingredients, oats and rice,
• provide vitamins A and B. The company wants to know how many ounces of oats and rice it should
• include in each box of cereal to meet the minimum
• req
• uirements of
• 45 milligrams of vitamin A and
• 13
• milligrams of vitamin B while minimizing cost
• . An ounce of oats contributes 10 milligrams of
• vitamin A and 2
• milligram of vitamin B, whereas an ounce of rice con
• tributes 6 milligrams of A
• and 3
• milligrams of B.
• An ounce o
• f oats costs $0.06
• , and an ounce of rice costs $0.03.
• Formulate a linear programming model for this problem.
• Solve the model by using graphical analysis.
• A Furniture
• Company produces chairs and tables from two resources
• -
• labor and wood. The
• company has 125
• hours of labor and 45
• board
• -
• of wood available each day. Demand for chairs is
• limited to 5 per day. Each chair requires 7 hours of labor and 3.5 board
• -
• of wood, whereas a table
• requires 14 hours of labor and 7 board
• -
• of wood. The profit derived f
• rom each chair is $325 and
• from each table, $120. The company wants to determine the number of chairs and tables to produce
• each day in order to maximize profit. Formulate a linear programming model for this problem.
• Formulate a linear programming model fo
• r this problem.
• Solve the model by using graphical analysis.
• (Do not round the answers)
• How much labor and wood will be unused if the optimal numbers of chairs and tables are
• produced?
• Kroeger supermarket sells its own brand of canned peas as well as
• several national brands. The
• store makes a profit of $0.28 per can for its own peas and a profit of $0.19 for any of the national
• The store has 6 square feet of shelf space available for canned peas, and each can of peas
• takes up 9 square inches of
• that space. Point
• -
• of
• -
• sale records show that each week the store never
• sales more than half as many cans of its own brand as it does of the national brands. The store
• wants to know how many cans of its own brand of peas of peas and how many cans of the nat
• ional
• brands to stock each week on the allocated shelf space in order to maximize profit.
• Formulate a linear programming model for this problem.
• Solve the model by using graphical analysis.
• MAT540 Homework
• Week
• 6
• Page
• 2
• of
• 2
• Solve the following linear programming model graphically:
• Minimize
• Z=8X
• 1
• + 6X
• 2
• Subject to
• 4X
• 1
• + 2X
• 2
• 20
• -
• 6X
• 1
• + 4X
• 2
• X
• 1
• + X
• 2
• X
• 1
• ,
• X
• 2