5 Which would decrease the demand for a particular type of labor?An increase in the prices of the resources that are complements to that type of laborAn increase in the wages of that type of laborXAn increase in the demand for the products produced by that type of laborA decrease in the prices of those resources that are complements for that type of labor

Demand for a type of good is the numerical way of representing what the consumers would purchase at…

Answered: Which would decrease the demand for a…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.6: Variation

Problem 10E

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In this application, we set up a mathematical model for determining the total costs in setting up a training program, such as a hospital might use. Then we use calculus to find the time interval between training programs that produces the minimum total cost. The model assumes that the demand for trainees is constant and that the fixed cost of training a batch of trainees is known. Also, it is assumed that people who are trained, but for whom no job is readily available, will be paid a fixed amount per month while waiting for a job to open up. The model uses the following variables. D = demand for trainees per month N = number of trainees per batch C1 = Fixed cost of training a batch of trainees C2 = marginal cost of training per trainee per month C3 = salary paid monthly to a trainee who has not yet been given a job after training m = time interval in months between successive batches of trainees t = length of training program in months Z(m) = total monthly cost of program The total cost of training a batch of trainees is given by C1+NtC2. However, N=mD, so that the total cost per batch is C1+mDtC2. After training, personnel are given jobs at the rate of D per month. Thus, ND of the trainees will not get a job the first month, N2D will not get a job the second month, and so on. The ND trainees who do not get a job the first month produce total costs of (ND)C3, and so on. Since N=mD, the costs during the first month can be written as. (ND)C3=(mDD)C3=(m1)DC3 While the costs during the second month are (m2)DC3, and so on. The total cost for keeping the trainees without a job is thus (m1)DC3+(m2)DC3+(m3)DC3++2DC3+DC3 Which can be factored to give DC3[(m1)+(m2)+(m3)++2+1] The expression in bracket is the sum of the terms of an arithmetic sequence, discussed in most algebra texts. Using formulas for arithmetic sequences, the expression in brackets can be shown to equal m(m1)2, so that we have DC3[m(m1)2](1) As the total cost for keeping jobless trainees. The total cost per batch is the sum of the training cost per batch. C1+mDtC2, and the cost of keeping trainees without a proper job, given by equation 1, since we assume that a batch of trainees is trained every m months, the total cost per month, Z(m), is given by Z(m)=C1+mDtC2m+DC3[m(m1)2]m=C1m+DtC2+DC3(m12) Source: P.I., Goyal and S.K. Goyal. Find Z(m)
Continued This is a continuation of Exercise 13. As we saw earlier, the stock turnover rate of an item is the number of times that the average inventory of the item needs to be replaced as a result of sales in a given time period. Suppose that a hardware store sells 80 shovels each year. a. Suppose that the hardware store maintains an average inventory of 5 shovels. What is the annual stock turnover rate for the shovels? How is this related to the yearly number of orders to the wholesaler needed to restock inventory? b. What would he the annual stock turnover rate if the store maintained an average inventory of 20 shovels? c. Write a formula expressing the annual stock turnover rate as a function of the average inventory of shovels, identify the function and the variable, and state the units.

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