linear programming

posted by .

Mountain Laurel Vineyards produces three kinds of wine Mountain Blanc, Mountain Red, and Mountain Blush. The company has 17 tons of grapes available to produce wine this season . A cask of Blanc requires 0.21 tons of grapes, a cask of Red requires 0.24 tons, and a cask of Blush requires 0.18 tons. The vineyard has enough storage space in its aging room to store 80 casks of wine.

The vineyard has 2,500 hours of production capacity, and it requires 12 hours to produce a cask of Blanc, 14.5 hours to produce a cask of Red, and 16 hours to produce a cask of Blush. From past sales the vineyard knows that demand for the Blush will be no more than half of the sales of the other two wines combined. The profit for a cask of Blanc is $7,500, the profit for a cask of Red is $8,200, and the profit for a cask of Blush is $10,500.

Formulate a linear programming model for this problem.

49. Solve the linear programming model formulated in Problem 46 for Mountain Laurel Vineyards by using the computer.

a. If the vineyard were to determine that the profit from Red was $7,600 instead of $8,200, how would that affect the optimal solution?

b. If the vineyard could secure one additional unit of any of the resources used in the production of wine, which one should it select?

c. If the vineyard could obtain 0.5 more tons of grapes, 500 more hours of production capacity, or enough storage capacity to store 4 more casks of wine, which should it choose?

d. All three wines are produced in the optimal solution. How little would the profit for Blanc have to be for it to no longer be produced?

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math

    if someone could please help that would be muchly appreciated. A group of mountain climbers are using trigonometry to find the height of a mountain located in the rockies. From point A, which is due west of the mountain, the angle …
  2. math

    angle of elevation of the top of a mountain to a man is 45degree.if we walk along a slope of 30 degree of the mountain 100 meters then the angle of elevation of the top of mountain becomes 60 degree.find the height of the mountain.
  3. linear programming

    Exeter Mines produces iron ore at four different mines; however, the ores extracted at each mine are different in their iron content. Mine 1 produces magnetite ore, which has a 70% iron content; mine 2 produces limonite ore, which …
  4. Trigonometry

    Height of a mountain While traveling across flat land, you notice a mountain directly in front of you. The angle of elevation to the peak is 2.5°. After you drive 18 miles closer to the mountain, the angle of elevation is 10°. Approximate …
  5. Biotech

    So our proposal in our biotech is all about wine, so I'm wondering, before, why do people usually use grapes in making wine and not using other sweet fruits like apple, or orange?
  6. Math

    a surveyor is 3 miles from a mountain. The angle of elevation from the ground to the top of the mountain is 15 degrees. What is the height of the mountain?
  7. llinear programming

    Mountain Laurel Vineyards produces three kinds of wineMountain Blanc, Mountain Red, and Mountain Blush. The company has 17 tons of grapes available to produce wine this season. Acask of Blanc requires 0.21 tons of grapes, a cask of …
  8. math

    There are 6 cyclists with red mountain bikes and 4 with green mountain bike at the race, what was the ratio of red to green mountain bikes?
  9. Applied calculus

    A geologist in Tibet discovers a new mountain in the area of Gyangtse. The equation of the mountain is given by f(x,y) = -x^4 - y^4 +2xy where x and y is measured in mile. What is the relative maximum height of the mountain in meters?
  10. precal 2

    At an altitude of 2000 feet, Ace is flying toward a mountain (a vertical rock face). If the angle of elevation from the plane to the top of the mountain is 20o and the angle of depression to the base of the mountain is 6o, then how …

More Similar Questions