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Answer :
1. The corner point representing the intersection of the two constraints is: B. Y is 500, X is 1500.
2. The ingredient III constraint is: C. 2B + 4C <= 4800.
3. The value of the objective function when X is 200 and Y is 1000 is: D. More than 10000.
4. The statement "If the right hand side of the constraint is increased to 120, then the objective function value will increase by 40" is: True.
1. For the first question:
To find the corner point representing the intersection of the two constraints, we need to solve the system of equations formed by the two inequalities.
The given constraints are:
3X + Y ≤ 3000
X + 3Y ≤ 5000
To find the intersection, we need to find the values of X and Y that satisfy both inequalities.
By solving the system of equations, we can find the corner point:
3X + Y = 3000 -- (1)
X + 3Y = 5000 -- (2)
Multiplying equation (1) by 3 and equation (2) by 1, we get:
9X + 3Y = 9000 -- (3)
X + 3Y = 5000 -- (4)
Subtracting equation (4) from equation (3), we have:
8X = 4000
X = 500
Plugging the value of X into equation (4), we get:
500 + 3Y = 5000
3Y = 4500
Y = 1500
Therefore, the corner point representing the intersection of the two constraints is:
X = 500, Y = 1500
So, the answer is:
B. Y is 500, X is 1500.
2. For the second question:
Let's represent the constraints in terms of ingredient III.
For Product B:
2 tablespoons of ingredient III are required for each B.
For Product C:
4 tablespoons of ingredient III are required for each C.
Since the company has 4800 tablespoons of ingredient III, the constraint can be written as:
2B + 4C ≤ 4800
So, the answer is:
C. 2B + 4C ≤ 4800.
3. For the third question:
The value of the objective function when X is 200 and Y is 1000 can be calculated as follows:
Objective function value = 2.25X + 2.60Y
= 2.25(200) + 2.60(1000)
= 450 + 2600
= 3050
So, the value of the objective function is 3050.
Therefore, the answer is:
D. More than 10000.
4. For the fourth question:
The statement is true.
The shadow price indicates how much the objective function value will change with a one-unit increase in the right-hand side (RHS) of the constraint. In this case, the shadow price is 2, which means that for every unit increase in the RHS of the constraint, the objective function value will increase by 2.
Given that the allowable increase in the sensitivity report is 20, increasing the RHS of the constraint from 100 to 120 should result in an increase of 2 * 20 = 40 in the objective function value.
To know more about corner point:
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