1. Global Corp. sells its output at the market price of $9 per unit. Each plant has the costs
shown below:
Units of Output
1
2
3
4
5
6
7
8 Total Cost ($)
9
11
15
21
29
39
51
65 How much output should each plant produce? Please specify your answer as an integer.
2. Suppose that you can sell as much of a product (in integer units) as you like
at $43 per unit. Your marginal cost (MC) for producing the qth unit is given by: MC=8q
This means that each unit costs more to produce than the previous one (e.g., the first
unit costs 8*1, the second unit (by itself) costs 8*2, etc.).
If fixed costs are $350, what is the optimal output level?
Please specify your answer as an integer. 3. Assume that a competitive firm has the total cost function: TC=1q^3−40q^2+740q+1600
Note: 1q is cubed and 40q is squared
Suppose the price of the firm's output (sold in integer units) is $650 per unit.
Using tables (but not calculus) to find a solution, how many units should the firm produce to
maximize profit?
Please specify your answer as an integer. 4. Assume that a competitive firm has the total cost function:
TC=1q^3−40q^2+820q+1900
Note: 1q is cubed and 40q is squared
Suppose the price of the firm's output (sold in integer units) is $600 per unit. Using calculus and formulas (but no tables and restricting your use of spreadsheets to
implementing the quadratic formula) to find a solution, how many units should the firm
produce to maximize profit?
Please specify your answer as an integer.
Hint: The first derivative of the total cost function is the marginal cost function.
Set the marginal cost equal to the marginal revenue (price in this case) to define an equation
for the optimal quantity q.
Rearrange the equation to the quadratic form aq^2 + bq + c = 0, where a, b, and c are
constants. Note: the aq is squared
Use the quadratic formula to solve for q:
For non-integer quantity, round up and down to find the optimal value.
5. Suppose a competitive firm has as its total cost function: TC=17+2q^2
Note: the 2q is squared Suppose the firm's output can be sold (in integer units) at $57 per unit.
Using calculus and formulas (but no tables or spreadsheets) to find a solution, how many
units should the firm produce to maximize profit?
Please specify your answer as an integer. In the case of equal profit from rounding up and
down for a non-integer initial solution quantity, enter the higher quantity. 6. Assume that a monopolist faces a demand curve for its product given by: p=120-1q Further assume that the firm's cost function is: TC=580+11q Using calculus and formulas (but no tables or spreadsheets) to find a solution, how much
output should the firm produce at the optimal price?
Round the optimal quantity to the nearest hundredth before computing the optimal price,
which you should then round to the nearest cent. Note: Non-integer quantities may make
sense when each unit of q represents a bundle of many individual items.
Hint: Define a formula for Total Revenue using the demand curve equation. Then take the
derivative of the Total Revenue and Total Cost formulas. Use these derivative equations to
perform a marginal analysis.

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