Question

1. What is the slope of 〖y=4x〗^0.5+10x^(2 ) when x=16?

2. What is the slope of y=〖100-6x〗^0.5 when x=6?

3. Given the demand function is q=〖(1200-2p)〗^0.5 What is the point elasticity of demand when quantity is 30? (hint: you should write p as a function of q and then take the derivative. Then use the elasticity formula.

4. Derive the TR and MR functions if q=200-0.4p. If TC=11q^3- 22q^2+30q+20 find the MC function.

5. If a firm faces TR and TC functions below at what output profit is Maximum

TR=300q-2q^2

TC=12q^3- 44q^2+60q+30

Answer #1

Question 1. Relate to the following maximization problem:
maximize z(x,y)=10x^0.5y^0.5 subject to the constraint
10x+5y=40.
A) What is the optimal value of x?
B) What is the optimal value of y?
C) What is the maximized value of z(x,y)?

- Find the derivative of the following functions:
(i) Y = X 3 – 8X 2 + 57X + 2 (1 mark)
(ii) TC = 0.04Q 3 – 0.9Q 2 + 10Q + 5 (1 mark)
- The following relations describe monthly demand and supply for
a computer support service
catering to small business:
Q d = 1,500 – 5 P
Q s = -500 + 5 P
Where Q is the number of business that need services and P...

For the demand curve Q=50−P, what is the own-price elasticity of
demand when P=16 2/3 (that is, 50/3)? Is demand elastic, inelastic,
or unit elastic at that point?
a) -0.5, inelastic
b) -1, unit elastic
c) -0.5, elastic
d) 33.3, inelastic
e) 33.3, elastic

Gilat's utility function is given by
U(x,y)=(x-2)0.5(y-8)0.5
for ? > 2 and ? > 8. The price of goods x and
y are ?? =$3 and ?? =$2.
When using the cheapest bundle that will yield a utility level
of ? =817, how much of good x will Gilat consume?
Enter a numerical value below. You may round to the
second decimal if necessary.

1. Let profit be Π
= TR – TC = (140*Q - .30*Q2) – (20*Q1.2).
What is total revenue when profit is maximized?
A.
TR= 6,473.23.
B.
TR= 8,292.43.
C.
TR= 9,235.61.
D.
TR= 10,432.42.
E.
TR= 12,992.46.
2. Consider the multiplicative demand function Q =
4*P-1.2. Suppose price is reduced from 8 to 7. What is
the marginal effect on quantity demanded of the one unit change,
that is, what is ΔQ from the one (1) unit change in...

Your pricing team has run an A/B test and determined that when
the price of your product is $300 the quantity demanded is 100
units. However, when the price is $200 quantity demanded is 150
units.
Your procurement and warehousing team has also provided a best
estimate of your costs. The fixed cost for rent is $1,000 / month.
The variable cost to procure and ship your product is 8Q + 2Q²
Answer the following questions:
Write out your demand...

1. Given the following functions which represent an open
economy: Consumption: C=100+0.8Y Investment: I= 50 Government
Expenditure: G=130 Exports: X=100 Imports: M=50+0.2Y Equilibrium:
Y=C+I+G+X-M a) determine the values of the equilibrium level of
income, and b) determine the values of C and M at the
equilibrium
2. Given the following functions: Consumption: C=50+0.8Y
Investment: I= 750 -30r Money supply: Ms=4000
Transaction-Precautionary demand for money: L1=100 Speculative
demand for money: L2=3825-20r Determine the values of the national
income (Y), and interest...

For the function y = 4sin(π/4x - π/2) -3 list when the average
rate of change is positive, negative, and zero, considering the
beginning of the interval to be x = 4.

The graph of
f(x)=−10x+e5sin(x)f(x)=−10x+e5sin(x)
is rotated counterclockwise about the origin through an acute
angle θθ. What is the largest value of θθ for which the rotated
graph is still the graph of a function? What about if the graph is
rotated clockwise?
To answer this question we need to find the maximal slope of
y=f(x)y=f(x), which is , and the minimal slope which
is .
Thus the maximal acute angle through which the graph can be rotated
counterclockwise is θ=θ= degrees.
Thus...

What is the partial derivative with respect to x of the function
?=4?+6?=4x^3+6y evaluated at x=2 and y=2?
a. 38
b. 32
c. 54
d. 48

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