linear programming

linear programming.

MAT540

Week 6 Homework

Chapter 2

1.      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 requirements 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 contributes 6 milligrams of A and 3 milligrams of B. An ounce of oats costs $0.06, and an ounce of rice costs $0.03.

a.    Formulate a linear programming model for this problem. b.    Solve the model by using graphical analysis.

2.      A  Furniture  Company  produces  chairs  and  tables  from  two  resources-  labor  and  wood.  The company has 125 hours of labor and 45 board-ft. 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-ft. of wood, whereas a table requires 14 hours of labor and 7 board-ft. of wood. The profit derived from 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.

a.    Formulate a linear programming model for this problem.

b.    Solve the model by using graphical analysis. (Do not round the answers)

c.   How  much  labor  and  wood  will  be  unused  if  the  optimal  numbers  of  chairs  and  tables  are produced?

3.      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 brands. 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 national brands to stock each week on the allocated shelf space in order to maximize profit.

a.    Formulate a linear programming model for this problem. b.    Solve the model by using graphical analysis.

4.       Solve the following linear programming model graphically:

Minimize Z=8X1 + 6X2

Subject to

4X1 + 2X2         20

-6X1 + 4X2

X1 + X2

X1 , X2

linear programming

Thanks for installing the Bottom of every post plugin by Corey Salzano. Contact me if you need custom WordPress plugins or website design.