Tim mixed 2 parts vinegar and 5 parts water to make a cleaning liquid. How many parts of vinegar did Tim mix with each part of w
2 answers:
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we have
<u>The system of equations</u>
-------> equation
-------> equation
Substitute equation in equation
subtract both sides
Divide by both sides
the solution is the point
therefore
the answer is
the solution to the system of equations is the point
Answer:
See expla below
Step-by-step explanation:
Given the demand function:
q = D (x) = 943 - 17 x
a) Find the elasticity:
Find the derivative of the demand function.
D'(x)= -17
Thus, elasticity expression is:
Elasticity expression =
b) At what price is the elasticity of demand equal to 1?
This means E(x) = 1
Substitute 1 for E(x) in the elasticity equation:
Cross multiply:
Collect like terms
x = 27.74
Elasticity at the price of demand = 1 is 27.74
c) At what prices is the elasticity of demand elastic?
This means E(x) > 1
Therefore,
Cross multiply:
Collect like terms
x > 27.74
The elasticity of demand is elastic at x > 27.74
d) At what prices is the elasticity of demand inelastic?
This means E(x) < 1
Therefore,
Cross multiply:
Collect like terms
x < 27.74
The elasticity of demand is inelastic at x < 27.74
e) At what price is the revenue a maximum:
Total revenue will be:
R(x) = x D(x)
= x (943 - 17x)
= 943x - 17x²
R(x) = 934 - 17x(price that maximizes total revenue)
Take R(x) = 0
Thus,
0 = 943 - 17x
17x = 943x
Total revenue is maximun at x= 27.74 per cookie
f) At x = 21 per cookie, find the price:
Thus,
R (21) = (943 * 21) - (17 * 21²)
= 19803 - 7497
= 12306
At x = 27.74, find the price:
R(27.74) = (943 * 27.74) - (17 - 27.74²)
= 26158.82 - 13081.63
= 13077.19
We can see the new price of cookie causes the total revenue to decrease.
Therefore, with a small increase in price the total revenue will decrease.