A company manufactures rope, and the total cost of producing r r feet of rope is C ( r ) C(r) dollars. What does it mean to say that C ( 2000 ) = 800 ? C(2000)=800? What are the units of C ′ ( r ) ? C′(r)? Suppose that C ( 2000 ) = 800 C(2000)=800 and C ′ ( 2000 ) = 0.35 . C′(2000)=0.35. Estimate C ( 2100 ) , C(2100), and justify your estimate by writing at least one sentence that explains your thinking. Do you think C ′ ( 2000 ) C′(2000) is less than, equal to, or greater than C ′ ( 3000 ) ? C′(3000)? Why? Suppose someone claims that C ′ ( 5000 ) = − 0.1 . C′(5000)=−0.1. What would the practical meaning of this derivative value tell you about the approximate cost of the next foot of rope? Is this possible? Why or why not?

Emily sold the following investments during the year: stock date purchased date sold sales price cost basis a. 1,000 shares dot com co. 03-21-2007 02-04-2018 $20,000 $5,000 b. 500 shares big box store 05-19-2017 01-22-2018 $8,200 $7,500 c. 300 shares lotta fun, inc. 10-02-2017 09-21-2018 $3,000 $4,500 d. 700 shares local gas co. 06-17-2017 11-11-2018 $14,000 $17,000 for each stock, calculate the amount and the nature of the gain or loss.

Suppose a firm faces a fixed price of output, 푝푝= 1200. the firm hires workers from a union at a daily wage, 푤푤, to produce output according to the production function 푞푞= 2퐸퐸12. there are 225 workers in the union. any union worker who does not work for this firm is guaranteed to find nonunion employment at a wage of $96 per day. a. what is the firm’s labor demand function? b. if the firm is allowed to choose 푤푤, but then the union decides how many workers to provide (up to 225) at that wage, what wage will the firm set? how many workers will the union provide? what is the firm’s output and profit? what is the total income of the 225 union workers? c. now suppose that the union sets the wage, but the firm decides how many workers to hire at that wage (up to 225). what wage will the union set to maximize the total income of all 225 workers? how many workers will the firm hire? what is the firm’s output and profit? what is the total income of the 225 union workers? [hint: to maximize total income of union, take the first order condition with respect to w and set equal to 0.]

An important application of regression analysis in accounting is in the estimation of cost. by collecting data on volume and cost and using the least squares method to develop an estimated regression equation relating volume and cost, an accountant can estimate the cost associated with a particular manufacturing volume. consider the following sample of production volumes and total cost data for a manufacturing operation. production volume (units) total cost ($) 400 4000 450 5000 550 5400 600 5900 700 6400 750 7000 compute b 1 and b 0 (to 2 decimals if necessary). b 1 b 0 complete the estimated regression equation (to 2 decimals if necessary). = + x what is the variable cost per unit produced (to 1 decimal)? $ compute the coefficient of determination (to 4 decimals). note: report r 2 between 0 and 1. r 2 = what percentage of the variation in total cost can be explained by the production volume (to 2 decimals)? % the company's production schedule shows 500 units must be produced next month. what is the estimated total cost for this operation (to 2 decimals)? $