Cost, Profit, Revenue
What is the formula for the profit function?
P(x) = R(x) - C(x)
What does Marginal mean?
The derivative, the instantaneous rate of change, the slope, or velocity.
Which of the following would you typically want to maximize or minimize?
Cost, Profit, Revenue, Area of Enclosure, Storage Costs, Volume of a Box, Harvest Size, Package Materials, Cost of Materials, Tax Revenue, Yield, Fencing, Inventory Costs, Illumination, Time.
Maximize: Profit, Revenue, Area of Enclosure, Volume of Box, Harvest Size, Tax Revenue, Yield, Illumination.
Minimize: Cost, Storage Costs, Package Materials, Cost of Materials, Fencing, Inventory Costs, Time.
What is Elasticity and what is the formula for it?
Measures how responsive demand is to price changes. Elastic means responsive and inelastic means unresponsive.
E(p)=-p*D'(p)/D(p) or E=-dq/dp *p/q
What does Break-Even mean?
When revenue equals cost.
R(x) = C(x)
or when P(x) = 0
Do we find marginal the same way for cost, profit, and revenue functions and if so, how do we do it?
Yes, take the derivative.
Give a summary of the generic steps needed to maximize or minimize an optimization problem.
1. Identify given quantities, unknown quantities and sketch a diagram if helpful.
2. Write a primary equation to be optimized.
3. Write a secondary equation that relates the variables if necessary, and use it to write primary equation in one variable.
4. Set derivative of primary equation equal to zero to find potential critical values.
5. Ensure a max or min by plugging in or using second derivative test.
If demand is elastic, then revenue will _________(increase or decrease) as prices increase. So, to increase revenue, we should __________(raise or lower) prices.
If demand is inelastic, then revenue will _________(increase or decrease) as prices increase. So to increase revenue, we should _______(raise or lower) prices.
decrease, lower.
increase, raise.
What is the formula for the cost function?
C(x) = Variable costs - Fixed costs
What is average cost, profit and revenue? Summarize how to find the average of these functions.
AC = C(x)/x
AP = P(x)/x
AR = R(x)/x
Divide the function by x.
At how many different x values can a function have an absolute maximum value? Give an example.
At every point in its domain. A constant function.
TRUE or FALSE:
Demand is elastic if E<1
Demand is inelastic if E>1
FALSE!!!!!!!!!!!
Elastic if E>1
Inelastic if E<1
What kind of cost frequently gets forgotten when building a cost function?
Fixed cost.
What is a way to approximate the marginal cost without taking the derivative?
C(x+1)-C(x)
When making a profit function, what is a typical mistake that students would make with the following problem:
R(x)-C(x)=(3x2+4x-1)-(2x2-4x+3)
Forgetting to distribute the minus sign when doing revenue - cost.
P(x) = 3x2+4x-1-2x2+4x-3
What is the formula for the Marginal Average Cost?
MAC(x)=AC'(x)=(C(x)/x)'
Basically the derivative of the average cost function.