Revenue, cost, and profit functions. A company manufactures 10- and 3-speed bicycles. The weekly demand and cost equations are p = 230 − 9 x + y q = 130 + x − 4 y C ( x , y ) = 200 + 80 x + 30 y where $ p is the price of a 10-speed bicycle, $ q is the price of a 3-speed bicycle, x is the weekly demand for 10-speed bicycles, y is the weekly demand for 3-speed bicycles, and C ( x , y ) is the cost function. Find the weekly revenue function R ( x , y ) and the weekly profit function P ( x , y ). Evaluate R (10, 15) and P (10, 15).
Revenue, cost, and profit functions. A company manufactures 10- and 3-speed bicycles. The weekly demand and cost equations are p = 230 − 9 x + y q = 130 + x − 4 y C ( x , y ) = 200 + 80 x + 30 y where $ p is the price of a 10-speed bicycle, $ q is the price of a 3-speed bicycle, x is the weekly demand for 10-speed bicycles, y is the weekly demand for 3-speed bicycles, and C ( x , y ) is the cost function. Find the weekly revenue function R ( x , y ) and the weekly profit function P ( x , y ). Evaluate R (10, 15) and P (10, 15).
Solution Summary: The author calculates the weekly revenue function R(x,y) and weekly profit function, using the equations that represent the price of 10-speed and 3-speed bicycles.
Revenue, cost, and profit functions. A company manufactures 10- and 3-speed bicycles. The weekly demand and cost equations are
p
=
230
−
9
x
+
y
q
=
130
+
x
−
4
y
C
(
x
,
y
)
=
200
+
80
x
+
30
y
where $p is the price of a 10-speed bicycle, $q is the price of a 3-speed bicycle, x is the weekly demand for 10-speed bicycles, y is the weekly demand for 3-speed bicycles, and C(x, y) is the cost function. Find the weekly revenue function R(x, y) and the weekly profit function P(x, y). Evaluate R(10, 15) and P(10, 15).
2) Consider the set SL(n, R) consisting of n x n matrices with real entries having de-
terminant equal to 1. Prove that SL(n, R) is a group under the operation of matrix
multiplication (it is referred to as the Special Linear Group).
1) What is the parity of the following permutation?
(1389) (24) (567)
4.7 Use forward and backward difference approximations of O(h)
and a centered difference approximation of O(h²) to estimate the
first derivative of the function examined in Prob. 4.5. Evaluate the
derivative at x = 2 using a step size of h = 0.2. Compare your results
with the true value of the derivative. Interpret your results on the
basis of the remainder term of the Taylor series expansion.
Chapter 7 Solutions
Calculus for Business, Economics, Life Sciences, and Social Sciences (14th Edition)
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