In a workshop, it costs $300 to make one piece of furniture. The second piece costs a

Chapter 13, Problem 12

(choose chapter or problem)

In a workshop, it costs $300 to make one piece of furniture. The second piece costs a bit less, $280. The third costs even less, $263, and the fourth costs only $249. The cost for each additional piece of furniture is called the marginal cost of production. Table 13.3 gives the marginal cost, c, and the change in marginal cost, c, in terms of the number of pierces of furniture, n. As the quantity produced increases, the marginal cost generally decreases and then increases again. a) Assume that the arithmetic sequence 20, 17, 14, . . . , continues. Complete the table for n = 5, 6, . . . , 12. (b) Find a formula for cn, the marginal cost for producing the nth piece of furniture. Use the fact that cn is found by adding the terms in an arithmetic sequence. Using your formula, find the cost for producing the 12th piece and the 50th piece of furniture. (c) A piece of furniture can be sold at a profit if it costs less than $400 to make. How many pieces of furniture should the workshop make each day? Discuss.