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ella [17]
3 years ago
11

Your business sells cupcakes in boxes of 10. The demand equation is

Mathematics
2 answers:
vampirchik [111]3 years ago
8 0
In Business, the following functions are important.
Revenue function = (price per unit) . (quantity of units) Symbols:
Cost function = (average cost per unit) . (quantity of units) Symbols:
Profit function = revenue − cost
Symbols:
Sometimes in a problem some of these functions are given. Note: Do not confuse p and P .
The price per unit p is also called the demand function p .
Marginal Functions:
The derivative of a function is called marginal function.
The derivative of the revenue function R(x) is called marginal revenue with notation: The derivative of the cost function C(x) is called marginal cost with notation:
The derivative of the profit function P(x) is called marginal profit with notation:
Example 1: Given the price in dollar per unit p = −3x2 + 600x , find: (a) the marginal revenue at x = 300 units. Interpret the result.
R=p.x
C=C.x
P=R−C
R′(x) = dR dx
C′(x) = dC dx
P′(x) = dP dx
revenue function: R(x) = p . x = (−3x2 + 600x) . x = −3x3 + 600x2 marginal revenue: R′(x) = dR = −9x2 + 1200x
dx
marginalrevenueat x=300 =⇒ R′(300)= dR =−9(300)2+1200(300)=−450000
dx x=300
Interpretation: If production increases from 300 to 301 units, the revenue decreases by 450 000 dollars.
(b) the marginal revenue at x = 100 units. Interpret the result. revenue function: R(x) = p . x = (−3x2 + 600x) . x = −3x3 + 600x2
marginal revenue: R′(x) = dR = −9x2 + 1200x dx
marginalrevenueat x=100 =⇒ R′(100)= dR =−9(100)2+1200(100)=30000 dx x=100
Interpretation: If production increases from 100 to 101 units, the revenue increases by 30 000 dollars.
melomori [17]3 years ago
5 0
Step by step equation
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A Chemist needs to mix a 20% acid solution with a 50% acid solution to obtain 15 liters of a 34% acid solution. How many liters
Nuetrik [128]

8 litres (amount of 20% solution needed) and 7 litres for (amount of 50% solution needed)

<u>Step-by-step explanation:</u>

Let consider ‘x’ for 20% acid solution and (15 – x) for 50% acid solution. And so, the equation would be as below,

                         20% in x + 50% in (15 – x) = 15 litres of 34%

Convert percentage values, we get

                              0.20(x) + 0.50 (15 – x) = 15 (0.34)

                              0.20 x + 7.5 – 0.50 x = 5.1

                              -0.3 x + 7.5 = 5.1

                              0.3 x = 7.5 – 5.1

                              0.3 x = 2.4

x = \frac{2.4}{0.3} = 8 litres (amount of 20 \% solution needed)

Apply ‘x = 8’ value in (15 – x) we get,

                         15 – 8 = 7 litres

The value of 7 litres for (amount of 50% solution needed)

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