Math assignment
Answergenie
math_exam.docx
a) What is the price per unit when there are 12 workers?
b) Determine the marginal revenue when there 12 workers:
c) Determine the marginal revenue product when there are 12 workers:
2.- A businessman thinks that for his product , the daily average product (hundreds of dollars), this is give by:
a) When the daily production increases, the average cost will approximate to a constant. Calculate this quantity.
b) Determine the marginal cost when 17 units are produced per day
c) The business man determined that if the productions and the sales increased to 18 units per day, the income would increase to $275.00. Should he increase the production?
3.- If the income and the total cost for a company are given by:
Where x is given in thousands of units and the cost and income are given in thousand money units. Find the number of units that optimize the utility and the value of such utility.
5.- A builder has to pay to install a grid circuit in the community center from the transformer located in a corner of the property. Due to the local law, the cable should be installed underground inside the community center. If the costs are $50 per meter along the street and $100 per meter underground. See figure 1. How far from the transformer should the cable be installed into the property to optimize the installation costs?
(
Transformer
) (
Underground
cable
)
6.- When a medicine is administered to a patient, the reaction (measured as the change of the blood pressure and temperature) can be exemplified with this equation:
Where c is a positive constant and m is quantity of medicine that it is absorbed in the blood when the reaction is maximum. The rate of change in respect with quantity of medicine it is called sensitivity.
a) Find the sensitivity, S.
b) Find the amount of medicine that it is absorbed in the blood when the sensitivity is maximum.
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7.- There are a distance of 15 miles between two industrial plants, they emit 75ppm y 300ppm respectively. Each plant has a restricted area with a radius of 1 mile, where nobody can build; the concentration of contaminants that arrive to any other point, Q, from any plant decreases as the reciprocal of the distance between that plant and the point Q.
Where should a house be located in the path between plants to minimize the total of contaminants that come from both plants?
8.- The equation of the demand is:
Where p is the sale price (in thousands of money units) per ton, when q tons of product are sold. The fixed price is $100 (thousand) and each ton costs $20 (thousand) to be produced. If the machinery has a capacity to produce 10 thousand tons. Define the production level that maximizes the utility. Find that maximum utility and the sale price per ton.
1000
3
50
+
=
q
q
I
18
19
5
35
324
2
+
+
+
=
q
q
C
1
3000
3000
)
(
+
-
=
x
x
I
2
12
500
)
(
x
x
x
C
+
+
=
x
÷
ø
ö
ç
è
æ
-
=
3
2
2
m
c
m
R
164
21
2
+
-
=
q
q
p
m
2
3
)
1
2
(
2
+
=
m
m
q
I
