SOLUTION: A food factory is making a beverage for a customer from mixing two different existing products A and B. The compositions of A and B and prices ($/L) are given as follows, Amount (

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: A food factory is making a beverage for a customer from mixing two different existing products A and B. The compositions of A and B and prices ($/L) are given as follows, Amount (      Log On


   

Question 1202370: A food factory is making a beverage for a customer from mixing two different existing products A and B. The compositions of A and B and prices ($/L) are given as follows,
Amount (L) in /100 L of A and B
Lime Orange Mango Cost ($/L)
A 2 6 4 4
B 7 4 8 12
The customer requires that there must be at least 5 Litres (L) Orange and at least 5 Litres of Mango concentrate per 100 Litres of the beverage respectively, but no more than 6 Litres of Lime concentrate per 100 Litres of beverage. The customer needs at least 140 Litres of the beverage per week.
a) Formulate a Linear Programming (LP) model for the factory that minimises the total cost of producing the beverage while satisfying all constraints.
b) Use the graphical method to find the optimal solution. Show the feasible region and the optimal solution on the graph. Annotate all lines on your graph.
c) What is the range for the cost ($) of A that can be changed without affecting the optimum solution obtained above?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
i get 140 liters of beverage A with a cost of 560.
here's the graph.

the cost of A was 4 dollars per liter.
the coswt of B was 12 dollars per liter.
the corner points of the feasible region are:
(76,64) = corner point 1
(140,0) = corner point 2
(300,0) = corner point 3
cost for corner point 1 was 76 * 4 + 64 * 12 = 1072
cost for corner point 2 was 140 * 4 = 560
cost for corner point 3 was 300 * 4 = 1200
sensitivity would be to keep raising the cosw for the x value until the minimum cost changes.
x is the number of liters of beverage A.
y is the number of liter of beverage B.
sensiivity analysis indidcates that the optimum solution will be change when the cost of beverage A increases to more than 12.00 per liter.
the following excel spreadsheet shows the sensiivity analysis.