Question

Assume that total benefit from a continuous decision, involving
a control variable Q, is: TB = 25Q – 2.5Q^{2} and the
associated total cost is: TC(Q) = 5 + 4Q^{2}.

With the total benefit and total cost functions (equations) given above:

Estimate the value of total benefit when the control variable Q is 3. Clearly show your steps and calculations.

Estimate the marginal benefit when the control variable Q is 3. Clearly show your steps and calculations.

Determine the level of control variable Q that maximizes total benefit. Clearly show your steps and calculations.

Provide a justification that total benefit is maximized at your determined level of control variable Q in (c) above.

Estimate the level of control variable Q that maximizes net benefits. Clearly show your steps and calculations.

Answer #1

The value of total benefit when the control variable Q is 3

TB = 25Q - 2.5Q^{2}

TB = 25 * 3 - 2.5 3^{2}

TB = 52.50

_________________________________________________________

TB = 25Q - 2.5Q^{2}

Marginal benefit is found by taking the derivative of total benefit

Marginal benefit = 25 - 5Q

Marginal benefit = 25 - 5 * 3

MB = 10

_____________________________________________________________________

The level of control variable Q that maximizes total benefit is found by equating marginal benefit and marginal cost equation

TC = 5 + 4Q^{2}

Marginal cost =8Q

8Q = 25 - 5Q

13Q = 25

Q = 2 units

___________________________________________________________________

Total benefit at the determined level of control variable Q =
25Q - 2.5Q^{2}

TB = 25 * 2 - 2.5*2^{2}

TB = 40

Complete the table below. Clearly show the basis for each column
estimates.
Control Variable
Total Benefits
Total Cost TC(Q)
Net Benefits NB(Q)
Marginal Benefit MB(Q)
Marginal Cost MC(Q)
Marginal Net Benefits
MNB(Q)
Q
TB(Q)
100
1200
900
250
80
102
1670
90
104
2110
100
106
2520
110
108
2900
120
110
3250
130
112
3570
140
114
3860
150
116
4120
160
118
4350
170
120
4550
180
At what level of the control variable are the net benefits...

Suppose that the total benefit and total cost from a continuous
activity are, respectively, given by the following equations:
B(Q) = 100 + 36Q –
4Q2 and C(Q) =80 + 12Q.
(Note: MB(Q) = 36 – 8Q and
MC(Q) = 12.)
Instructions: Use a negative sign (-) where
appropriate.
a. Write out the equation for the net benefits.
N(Q) = ______________
+________________ Q
+________________ Q2
b. What are the net benefits when Q = 1? Q =
5?
Net benefits when Q...

1.Suppose that the total benefit depends on the level Q of a
particular activity with total benefits given by B(Q) = 40Q - Q 2
and total costs given by C(Q) = 300 + 20Q
a. Write out the equation for net benefits.
b. What are net benefits when Q = 3? Show calculations.
c. Write out the equation for marginal net benefits.
d. What are the marginal net benefits when Q = 3
e. Can you infer from your...

9. Average cost in the long-run is defined as _____.
TVC/Q
TC/Q
TVC + TFC/Q
none of the above
10. Economies of scale is a characteristic of production where
______.
average costs increase as output increases
total cost decreases as output increases
average cost decreases as output increases
average cost decreases as output decreases
11. Which of the following factors of production is more likely
to be fixed in the short run?
The number of workers.
Changes in electricity consumed....

Quantity of Lanterns
Fixed Cost ($)
Variable Cost ($)
Total Cost ($)
Average Total Cost ($)
50
250
250
500
10.00
75
250
390
640
8.53
90
250
522
772
8.58
120
250
714
964
8.03
150
250
1049
1299
8.66
200
250
1600
1850
9.25
210
250
2100
2350
11.19
The table above shows cost data for a producer of lighting
fixtures. Answer the questions using the information shown in the
table and show your calculations.
1. What is...

There are different methods of separating the
fixed cost portion from the variable cost portion...as discussed in
your textbook. We will discuss only one of those methods, the
High-Low Method.
Let's say that the monthly electricity costs at your
company are listed below:
Machine-Hours
Electricity Cost
March
413
$73,710
April
506
$77,400
May
435
$74,470
June
486
$76,600
July
499
$77,040
August
461
$75,630
September
467
$75,710
October
458
$75,220
November
425
$74,030
Why is the above a mixed cost?...

. Assume that the CDE Company has yearly Fixed costs of $30,000
and its Variable costs are $30,000, which are 60% of its Sales.
Calculate:
[Use ONLY formula for your calculations. Do NOT use
algebra]
Question:
Its profit or loss when its total sales are $110,000.
b. The sales level (dollars) required
to break-even.
c. The sales needed to make a profit of
$35,000.
2. ABC Company manufactures and distributes Product A. An
extract from the 20X5 statement...

As CEO of Ocean World, Rita Greenwood knows it is important to
control costs and to respond quickly to changes in the highly
competitive boat-building industry. When DMG Consulting proposes
that Ocean World invest in an ERP system, she forms a team to
evaluate the proposal: the plant engineer, the plant foreman,
the systems specialist, the human resources director, the
marketing director, and the management accountant. A month later,
management accountant Marcus Chumura reports that the team and DMG
estimate...

Several years ago, Westmont Corporation developed a
comprehensive budgeting system for planning and control purposes.
While departmental supervisors have been happy with the system, the
factory manager has expressed considerable dissatisfaction with the
information being generated by the system.
A report for the company's Assembly Department for the month of
March follows:
Assembly Department
Cost Report
For the Month Ended March 31
Actual Results
Planning Budget
Variances
Machine-hours
15,000
20,000
Variable costs:
Supplies
$
8,700
$
9,300
$
600
F...

Several years ago, Westmont Corporation developed a
comprehensive budgeting system for planning and control purposes.
While departmental supervisors have been happy with the system, the
factory manager has expressed considerable dissatisfaction with the
information being generated by the system.
A report for the company's Assembly Department for the month of
March follows:
Assembly Department
Cost Report
For the Month Ended March 31
Actual Results
Planning Budget
Variances
Machine-hours
25,000
30,000
Variable costs:
Supplies
$
6,600
$
7,200
$
600
F...

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