Aleksandra
New member
Hi there,
I have a homework problem with my business decision models course. I have a typical Maximizing Profit question which has one solution. There is a part of the question that goes like this:
There is a single optimal solution to this problem. However, if the objective function had been parallel to one of the constraints, there would have been two equally optimal solutions. If the profit of X1 remains $50, what profit of X2 would cause the objective function to be parallel to to the space area constraint? Explain how you determined this.
So the question is this and here is the data given:
X1-Number of large rental spaces built
X2-Number of small rental spaces built
Maximized monthly earnings :
Z= 50X1 + 20X2
Constraints:
2X1 + 4X2 <= 400 (advertising budget)
100 X1 + 50X2 <= 8000 (space area)
x1<= 60 (rental limit expected)
x1, x2>= 0
I solved the question and found the optimal solution - 40 for x1 and 80 for x2 and graphed it but I have no idea how to find what profit for each X2 the company must have for the question to get two optimal solution. I know the isoprofit line has to be parallel to one of the constraints but that doesn't help me get the answer. If someone can help me and explain it I ll be EXTREMELY grateful!
THANK YOU!!!!!
I have a homework problem with my business decision models course. I have a typical Maximizing Profit question which has one solution. There is a part of the question that goes like this:
There is a single optimal solution to this problem. However, if the objective function had been parallel to one of the constraints, there would have been two equally optimal solutions. If the profit of X1 remains $50, what profit of X2 would cause the objective function to be parallel to to the space area constraint? Explain how you determined this.
So the question is this and here is the data given:
X1-Number of large rental spaces built
X2-Number of small rental spaces built
Maximized monthly earnings :
Z= 50X1 + 20X2
Constraints:
2X1 + 4X2 <= 400 (advertising budget)
100 X1 + 50X2 <= 8000 (space area)
x1<= 60 (rental limit expected)
x1, x2>= 0
I solved the question and found the optimal solution - 40 for x1 and 80 for x2 and graphed it but I have no idea how to find what profit for each X2 the company must have for the question to get two optimal solution. I know the isoprofit line has to be parallel to one of the constraints but that doesn't help me get the answer. If someone can help me and explain it I ll be EXTREMELY grateful!
THANK YOU!!!!!