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Question 1186852: LINEAR PROGRAMMING
The campus store sells dessert, Sobolo drink and Brukina drink. The Sobolo cost GH₵1.90 and the Brukina cost GH₵2.25. They sell the Sobolo drink for GH₵5.00 and the Burukina for GH₵6.00. They can obtain no more than 100 Sobolo and 75 Burukina per week. To meet the demands, they have to sell a total of at least 120 of the two drinks together. They cannot package more than 150 per week.
(i) Formulate this problem in terms of determining the profit- maximizing combination of the two drinks.
(ii) Solve the problem graphically.
(iii) How many of each should they sell to maximize profit?
(iv) Which constraints are binding?
(v) Determine the slack materials
(vi) Interpret your answers obtained in (v) above.
Answer by ikleyn(52787)   (Show Source):
You can put this solution on YOUR website! .
LINEAR PROGRAMMING
The campus store sells dessert, Sobolo drink and Brukina drink.
The Sobolo cost GH₵1.90 and the Brukina cost GH₵2.25.
They sell the Sobolo drink for GH₵5.00 and the Brukina for GH₵6.00.
They can obtain no more than 100 Sobolo and 75 Brukina per week.
To meet the demands, they have to sell a total of at least 120 of the two drinks together.
They cannot package more than 150 per week.
(i) Formulate this problem in terms of determining the profit- maximizing combination of the two drinks.
(ii) Solve the problem graphically.
(iii) How many of each should they sell to maximize profit?
(iv) Which constraints are binding?
(v) Determine the slack materials
(vi) Interpret your answers obtained in (v) above.
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This problem is very simple and admits very simple MENTAL solution.
This mental solution is much more educative than formal Linear Programming solution.
Therefore, I place here this mental solution, which require common sense and nothing more.
One Sobolo drink creates the profit of 5.00-1.90 = 3.10.
One Brukina drink creates the profit of 6.00-2.25 = 3.75.
So, let's apply the most aggressive strategy: will sell Brukina drinks as many as possible
in accordance with constraints, and then will sell Sobolo drinks as many as possible
in accordance with the remaining constraints.
According to constraints, we can solve 75 Brukina and we can not solve more Brukina due to the constrain 75.
OK, so we sell 75 Brukina.
Then the other constrain (150 for both) says that we can sell only 75 = 150 - 75 Sobolo.
It meets another constraint for Sobolo and for both, so we are OK to do it.
Thus the optimal solution is 75 Brukina and 75 Sobolo, that give the total profit of
75*(3.10 + 3.75) = 513.75.
All other constraints are satisfied.
ANSWER. The optimal solution is 75 Brukina and 75 Sobolo, that give the total profit of GH₵513.75.
Solved.
To further mock the authors, I will notice that in one part of the problem's condition they use the name Brukina,
while in other part of problem's condition they use the name Burukina, so I conclude
that they do not know the right name, and moreover, using a consistent name is not their priority.
To be consistent, I used the name Brukina consistently in the course of my solution.
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