Now suppose that the supply of new homes put on the market dropped, but price still stayed the same at $200,000. this could on
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Answer: Graph of (A) (B) and {D) are attached accordingly.
Explanation:
A)
The critical region of the constraints can be seen in the following diagram -
(0,9) (0,5) (0,3) (0,0) (3,0) (5,0) (9,0) The feasible region is shown in white
The intersection points are found by using these equations -
Vertex Lines Through Vertex Value of Objective
(3,2) x+3y = 9; 2x+2y = 10 48
(9,0) x+3y = 9; y = 0 72
(2,3) 2x+2y = 10; 6x+2y = 18 52
(0,9) 6x+2y = 18; x = 0 108
So, we can see the minimum value of the objective function occurs at point (3,2) and the minimum value of the objective function is = 48.
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B)
When we change the coefficients of the variables in the objective function, the optimal solution may or may not change as the weights (coefficient) are different for each constraints for both the variabls. So, it all depends on the coefficient of the variables in the constraints.
In this case, the optimal solution does not change on changing the coefficient of X from 8 to 6 in the objective function.
The critical region would remain same (as shown below) as it is defined by the constraints and not the objective function.
(0,9) (0,5) (0,3) (0,0) (3,0) (5,0) (9,0) The feasible region is shown in white
However, the optimal value of the objective function would change as shown below-
Vertex Lines Through Vertex Value of Objective
(3,2) x+3y = 9; 2x+2y = 10 42
(9,0) x+3y = 9; y = 0 54
(2,3) 2x+2y = 10; 6x+2y = 18 48
(0,9) 6x+2y = 18; x = 0 108
So, we can see that the minimum value now has become 42 (which had to change obviously).
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C)
Now, when we change the coefficient of the variable Y from 12 to 6, again the critical region would remain same as earlier. But in this case, the optimal solution changes as shown below -
Vertex Lines Through Vertex Value of Objective
(3,2) x+3y = 9; 2x+2y = 10 36
(9,0) x+3y = 9; y = 0 72
(2,3) 2x+2y = 10; 6x+2y = 18 34
(0,9) 6x+2y = 18; x = 0 54
We can see that the minimum value now occurs at (2,3) which is 34, so both the optimal solution and optimal value have changed in this case.
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D)
When we limit the range of the variables as -
4 \leq X \leq 8 \:\: and\:\: 12\leq Y \leq 24,
the critical region now becomes -
So, the new critical points are (4,12), (4,24), (8,24) and (8,12).
So, the values of the objective function at these points can be calculated as -
Vertex Value of Objective
(4,12) 8*4+12*12 = 176
(4,24) 8*4+12*24 = 320
(8,24) 8*8+12*24 = 352
(8,12) 8*8+12*12 = 208
So, the new optimal solution is (4,12) and the optimal value is 176.
if we knew the range of the variables in the part B and C earlier, we could have just said that the optimal solution will not change as the value would have been no longer depended on the coefficients of variables in the constraints.
Answer:
The first five terms of the sequence are:
First year: $3270.00
Second year: $3564.30
Third year: $3885.09
Fourth year: $4234.75
Fifth year: $4615.87
Explanation:
When we're dealing with compound interest rates we're dealing with interests being re-invested into the original investment. This means that the new interests of one period will bear interests in the next period. This can be simply calculated using the compound interest formula.
The formula for compound interest rates is
Where:
<em>P</em> is the principal amount being invested,
<em>i</em> is the interest rate,
<em>n</em> is the number of years.
So for the first year we replace in the formula with the given values:
3000 × = $3270
And for the rest of the years we only need to modify the value of <em>n</em>.
For the second year we'd have:
3000 × = $3564.3
And so on.
Answer: P1
Explanation:
In the long-run and even without government intervention, the economy will eventually converge on its long run equilibrium level which is the full employment output level of Q1.
This means that eventually, the aggregate demand in this scenario will go down to AD1 or AS would change such that the long run price will go to P1 as this is the full employment output price level.
