1. Write a linear cost function for each situation. Identify all variable used.
A parking garage charges 50 cents plus 35 cent per half-hour
2. Find the cost function in each case. Marginal cost: $90; 150 items cost $16,000 to produce.
3. Supply and Demand: Let the supply and demand functions for butter pecan ice cream be given by
p= S(q)=2/5q and p=D(q) = 100-2/5q
where p is the price in dollars and q is the number of 10-gallon tubs
a). Graph these on the same axes
b) Find the equilibrium quantity and the equilibrium price.
4. Marginal cost of Coffee: The manager of a restaurant found that the cost to produce 100 cups of coffee is $11.02 while the cost to produce 400 cups is $40.12
Assume the cost C(x) is a linear function of x, the number of cups produced.
a). Find a formula for C (x)
b). What is the fixed cost?
c). Find the total cost of producing 1000 cups
d). Find the total cost of producing 1001st cups
e). Find the marginal cost of the 1001st cup
f). what is the marginal cost of any cup and what does this mean to the manager?
5. Break-Even Analysis: To produce x units of a religious medal costs C(x) = 12x +39 The revenue is R(x) = 25x. Both C(x) and R(x) are in dollars
a) Find the break-even quantity
b). Find the profit from 250 units
c) Find the number of units that must be produced for a profit of $130.
Please see the attached file for detailed solutions.
1. Assume the parking time is x hours. Then the cost in dollars is
C = ...
The solution is comprised of detailed explanations on cost function, such as marginal cost and break-even analysis. It also shows how to find the equilibrium price and quantities from supply and demand functions.