Cost, revenue, and profit rates. Repeat Problem $33$ for

$$\begin{aligned} C&=72,000+60x \quad R=200x-\frac{x^2}{30}\\ P&=R-C \end{aligned}$$

where production is increasing at a rate of $500$ calculators per week at a production level of $1,500$ calculators.

Use the following production possibilities frontier for a country to answer the questions.

Which point or points are efficient? Briefly explain why.

A manufacturer estimates that the hourly cost of producing x units of a product on an assembly line is $C(x)=.1 x^3-6 x^2+136 x+200$ dollars.

(a) Compute C(21)-C(20), the extra cost of raising the production from 20 to 21 units.

(b) Find the marginal cost when the production level is 20 units.

Your brother-in-law, Fred Miles, has just taken a new position as the plant manager of a local production facility. He has been told that the company uses a balanced scorecard approach to evaluate its managers. Fred is not familiar with this approach because his previous experience as a production manager focused only on whether the plant met the company's budgeted production.

Required:

1. Briefly explain to Fred how performance evaluations at his new company will differ from those at his previous company.
2. Give Fred five possible objectives that the new company will use in addition to production level in evaluating his performance. For each objective that you identify, be sure to indicate a plausible metric for measuring it.

You work in a semiconductor production plant that relies on several chlorofluorocarbons in its manufacturing process. One day, you find an unlabeled gas cylinder, and you are assigned to figure out what is in the tank. First you fill a 1.000-L flask with the gas. At a pressure of 250.0 torr and a temperature of 25.00 degree C, you determine that the mass of the gas in the flask is 2.2980 g. Then you send the flask to an outside lab for elemental analysis, and they report that the gas contains 14.05% C, 44.46% F, and 41.48% Cl by mass. Find the molecular formula of this gas.

Cobb–Douglas production function. If an industry invests $x$ thousand labor-hours, $10\leq{x}\leq20$, and $y$ million, $1\leq{y}\leq2$, in the production of $N$ thousand units of a certain item, then $N$ is given by

$$N(x,y)=x^{0.75}y^{0.25}$$

What is the average number of units produced for the indicated ranges of $x$ and $y$? Set up a double integral and evaluate it.

Show events that led to the cotton boom and to list the effects of increased cotton production on slavery and the southern economy.

In the following, name the term defined or answer the question.

The Toyota Production System is founded on these two philosophies.

What organism is involved in the production of Swiss cheese, and what products does it make that help to flavour the cheese and make the holes?

Look at Note 30.2, “Retirement Benefits.” AF incorporates estimates regarding staff turnover, life expectancy, salary increase, retirement age, and discount rates. How did AF report changes in these assumptions? Is that reporting method the same or different from the way we report changes under U.S. GAAP?

Carlos Cavalas, the manager of Echo Products’ Brazilian Division, is trying to set the production schedule for the last quarter of the year. The Brazilian Division had planned to sell 3,600 units during the year, but by September 30 only the following activity had been reported:

The division can rent warehouse space to store up to 1,000 units. The minimum inventory level that the division should carry is 50 units. Mr. Cavalas is aware that production must be at least 200 units per quarter in order to retain a nucleus of key employees. Maximum production capacity is 1,500 units per quarter.

Demand has been soft, and the sales forecast for the last quarter is only 600 units. Due to the nature of the division’s operations, fixed manufacturing overhead is a major element of product cost.

Required:

1. Assume that the division is using variable costing. How many units should be scheduled for production during the last quarter of the year? (The basic formula for computing the required production for a period in a company is: Expected sales 1 Desired ending inventory 2 Beginning inventory 5 Required production.) Show computations and explain your answer. Will the number of units scheduled for production affect the division’s reported income or loss for the year? Explain.

2. Assume that the division is using absorption costing and that the divisional manager is given an annual bonus based on divisional operating income. If Mr. Cavalas wants to maximize his division’s operating income for the year, how many units should be scheduled for production during the last quarter? [See the formula in (1) above.] Explain.

3. Identify the ethical issues involved in the decision Mr. Cavalas must make about the level of production for the last quarter of the year.

What is meant by the term equivalent units of production when the weighted-average method is used?

Regarding Target’s audit report:

a. Who is Target’s auditor?
b. Did Target receive a “clean” (unmodified) audit opinion?

Why do companies that implement Lean Production tend to have minimal inventories? Explain briefly.