Use Table 1 to evaluate all integrals involved in any solutions of Problems 71–94. 88. Revenue. The marginal revenue for a Company that manufactures and sells x graphing calculators per week is given by R ′ ( x ) = x 1 + 2 x R ( 0 ) = 0 where R ( x ) is the revenue in dollars. Find the revenue func- tion and the number of calculators that must be sold (to the nearest unit) to produce $10,000 in revenue per week. How inuch weekly revenue (to the nearest dollar) will the Company have if 1,000 calculators are sold per week?
Use Table 1 to evaluate all integrals involved in any solutions of Problems 71–94. 88. Revenue. The marginal revenue for a Company that manufactures and sells x graphing calculators per week is given by R ′ ( x ) = x 1 + 2 x R ( 0 ) = 0 where R ( x ) is the revenue in dollars. Find the revenue func- tion and the number of calculators that must be sold (to the nearest unit) to produce $10,000 in revenue per week. How inuch weekly revenue (to the nearest dollar) will the Company have if 1,000 calculators are sold per week?
Solution Summary: The author calculates the revenue function and the number of calculators that must be sold that generates 10,000 per week. They also calculate the weekly revenue that the agency will have on the sale of 1,000 calculations.
Use Table 1 to evaluate all integrals involved in any solutions of Problems 71–94.
88. Revenue. The marginal revenue for a Company that manufactures and sells x graphing calculators per week is given by
R
′
(
x
)
=
x
1
+
2
x
R
(
0
)
=
0
where R(x) is the revenue in dollars. Find the revenue func- tion and the number of calculators that must be sold (to the nearest unit) to produce $10,000 in revenue per week. How inuch weekly revenue (to the nearest dollar) will the Company have if 1,000 calculators are sold per week?
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
1 (Expected Shortfall)
Suppose the price of an asset Pt follows a normal random walk, i.e., Pt =
Po+r₁ + ... + rt with r₁, r2,... being IID N(μ, o²).
Po+r1+.
⚫ Suppose the VaR of rt is VaRq(rt) at level q, find the VaR of the price
in T days, i.e., VaRq(Pt – Pt–T).
-
• If ESq(rt) = A, find ES₁(Pt – Pt–T).
2 (Normal Distribution)
Let rt be a log return. Suppose that r₁, 2, ... are IID N(0.06, 0.47).
What is the distribution of rt (4) = rt + rt-1 + rt-2 + rt-3?
What is P(rt (4) < 2)?
What is the covariance between r2(2) = 1 + 12 and 13(2) = r² + 13?
• What is the conditional distribution of r₁(3) = rt + rt-1 + rt-2 given
rt-2 = 0.6?
3 (Sharpe-ratio) Suppose that X1, X2,..., is a lognormal geometric random
walk with parameters (μ, o²). Specifically, suppose that X = Xo exp(rı +
...Tk), where Xo is a fixed constant and r1, T2, ... are IID N(μ, o²). Find
the Sharpe-ratios of rk and log(Xk) — log(Xo) respectively, assuming the
risk free return is 0.
Chapter 6 Solutions
Calculus for Business, Economics, Life Sciences, and Social Sciences (13th Edition)
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