1. A company can produce a maximum of 1500 widgets in a
year. If they sell x widgets during the year then their profit, in dollars, is given
by,
How many widgets should they try to sell in order to
maximize their profit? [Solution]
2. A management company is going to build a new apartment
complex. They know that if the complex
contains x apartments the maintenance
costs for the building, landscaping etc. will be,
The land they have purchased can hold a complex of at most
500 apartments. How many apartments should
the complex have in order to minimize the maintenance costs? [Solution]
3. The production costs, in dollars, per day of producing x widgets is given by,
What is the marginal cost when and ? What do your answers tell you about the
production costs? [Solution]
4. The production costs, in dollars, per month of producing x widgets is given by,
What is the marginal cost when and ? What do your answers tell you about the
production costs? [Solution]
5. The production costs, in dollars, per week of producing x widgets is given by,
and the demand function for the widgets is given by,
What is the marginal cost, marginal revenue and marginal
profit when and ? What do these numbers tell you about the
cost, revenue and profit? [Solution]