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Answer:
- f(x) = -0.15x^2 +19.8x -11 . . . profit function
- $642.40 maximum daily profit
- 66 gallons sold
- $10.90 per gallon
Step-by-step explanation:
<u>Given</u>:
daily cost function c(x) = x +11
price-demand function p(x) = -0.15x +20.8
<u>Find</u>:
daily profit function
maximum daily profit
quantity sold for maximum profit
price for maximum profit
<u>Solution</u>:
The revenue is the product of price and demand:
x·p(x) = -0.15x^2 +20.8x
The profit is the difference between revenue and cost:
f(x) = x·p(x) -c(x) = -0.15x^2 +20.8x -x -11
f(x) = -0.15x^2 +19.8x -11 . . . . . daily profit function
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The maximum profit will be had a the vertex of the curve, found where ...
x = -(19.8)/(2(-0.15)) = 66
f(66) = (-0.15·66 +19.8)66 -11 = 9.9·66 -11 = 642.40
The maximum profit is $642.40, when 66 gallons of ice cream are sold.
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The price that will result in demand of 66 gallons of ice cream is ...
p(66) = -0.15(66) +20.8 = 10.9
The price to charge per gallon to maximize profit is $10.90.
Answer: 150
Step-by-step explanation:
A fixed cost is referred to as a cost that does not change with the output level that is, it doesn't change when there is a rose or reduction in the amount of goods or services that are produced.
Since the total cost function is given as
TC=3Q³ - 5Q² + 4Q + 150, we can infer that from the equation the fixed cost is 150 while the variable cost is 3Q³ - 5Q² + 4Q
Answer:
the answer is sphere A: has a radius of4
Answer: Slope is -2
Step-by-step explanation:
Y² - Y¹ divide by X² - X¹
= 1 - 5 divide by 5 - 3
= -4/2
Slope is -2