47098978 11012-005 F17 Intuitive Caloulus Luke Covert 1001/17 11:12AM Homework:

Question

47098978 11012-005 F17 Intuitive Caloulus Luke Covert 1001/17 11:12AM Homework: H.W. 4.6 Optimization Part 2 Score: 0 of 1 p Bus Econ 4.6.37 Save 4 of 7 (0 complete) Hw Score: 0%, 0 of 7 pts EQuestion Help A manufacturer of hospital supplies has a unform annual demand for 500,000 boxes of bandages iIt costs $20 to store one box of bandages for one year and $320t set up the pliant for production How many times a year should the company produce boxes of bandages in order to minimice the total storage and selup costs? The company should produce boxes o bandages tmes)ayear Enter your answer in the answer box and then cick Check Answer

Explanation / Answer

Solution:

Assume "store one year" means 365 box-days and not "a year or part thereof".

k=500000 boxes/year
= 500000/365 boxes/day
= 1369.86 boxes/day

If supplies are produced every n days, then it must produce nk boxes at each production, and storage requirements are
P=(0+1+2+3+...n-1)k box-days for each production
=> P=(n/2)*(0+n-1)k=n(n-1)k/2 box-days/production

Over the whole year, there are 365/n productions, so total cost is
C(n)=320(365/n)+20(P/365)*(365/n)
=320*(365/n)+20(n-1)k/2

To minimize cost, C'(n)=0

=> C'(n)=-116800/n²+10k

Plug C'(n) = 0 and solve for n we get

=> n=2.92,
so to minimize cost the manufacturer must produce bandages

N=365/2.92 =125

=125 times a year

Answer: the manufacturer must produce bandages 125 times a year

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