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please do 1-6

, A Total Model for a Training Program In this application, we set up a mathematical model for determining the t s in setting up a am. Then we use calculus to find the time interval betweeng 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 C,-fixed cost of training a batch of trainees C2-marginal cost of training per trainee per month 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 C Z(m) = total onthly cost of prog. The total cost of training a batch of trainees is given by C+NtC. However. N mD, so that the total cost per batch is ci mDtC2 After training. personnel are given jobs at the rate of D er month. Thus, N -D of the trainees will not get a job the first month. N-2D will not get a job the second month, and so on The N - D trainees who do not get a job the first month produce total costs of (N -D)c, those not getting jobs during the second month produce costs of (N- 2D)c, and so on. Since N-mD the costs during the first month can be written as (N - D)C3 (mD -D)C (m-1)DC while the costs during the second month are (m-2)DC, and so on. The total cost for keeping (m- 1DC, + (m-2)DC + (m-3)DC + ...+ 2DCs + DC DC1(m-1) + (rn-2) + (rn-3) + .." + 2 + 2] the trainees without a job is thus Which can be factored to give The expression in brackets is the sum of the terms of an arithmetic sequence, di algebra texts. Using formulas for arithmetic sequences, the expression in brackets can be shown to equalso that we have in most m(m - 1) DC3 Equation (1) As the total cost for keeping jobless trainees. The total cost per batch is the sum of the training cost per batch. C+mDtC, and the cost of keeping trainees without a proper job, given be 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 -on + DtC2 + DCs(n21) I7t 1. Find Z'(m). 2. Solve the equation Z (m)-o. As a practical matter, it is usually required that m be a whole number. If m does not come out to be a whole number, then m+ and m" the two whole numbers closest to m, must be chosen. Calculate both z(m) and z(m);: the smaller of the two provides the optimum value of Z. 3. Suppose a company finds that its demand for trainees is 3 per mouth, that a training program requires 12 months, that the fixed cost of training a batch of trainees is $15.000. that the marginal cost per trainee per month is $100, and that trainees are paid $900 per month after training but before going to work. Use your result from Exercise 2 and find m. 4. Since m is not a whole number, find m+ and m 5. Calculate z(mt) and z(m) With Cheg + 249176/assignments/7368989 Page of 5 5. Calculate Z(m+) and z(m) What is the optimum time interval between successive batches of trainees? How many trainees should be in a batch? 6.

Answer 1

to jvenク iwn calo m-1 DC3 The '(m)- Solution DC3 -t 2. aC DC DC 3

20 botch- $15000 $loo 900 . J.T 乡ทา-.).aka -J 3 yeqoe 3. 3333

3 81 Since h, is not a ω}ole numb Si 19000 3X12X100 4 31400 u Sincol t 3X1+310 2. 15000 500 3600+&100 =|$11300 6.6