A chemical firm produces sodium bisulfate in 100-pound bags. Demand for this pro
ID: 402460 • Letter: A
Question
A chemical firm produces sodium bisulfate in 100-pound bags. Demand for this product is 30 tons per day. The capacity for producing the product is 50 tons per day. Setup costs $100, and storage and handling costs are $6 per ton a year. The firm operates 200 days a year. (Note: 1 ton = 2,000 pounds.)
How many bags per run are optimal? (Round your answer to the nearest whole number.)
What would the average inventory be for this lot size? (Round your intermediate calculations to 2 decimal places and final answer to the nearest whole number.)
Determine the approximate length of a production run, in days. (Round your intermediate calculations to 2 decimal places and final answer to the nearest whole number.)
About how many runs per year would there be? (Round your intermediate calculations to 2 decimal places and final answer to the nearest whole number.)
How much could the company save annually if the setup cost could be reduced to $39 per run? (Round your intermediate calculations and final answer to 2 decimal places. Omit the "$" sign in your response.)
How many bags per run are optimal? (Round your answer to the nearest whole number.)
Explanation / Answer
p=50/ton/day
u =30 tons/day
200 days/yr
D= 200*30=6000tons/yr
S= $100
H= $6/ton per yr
a) Qo=sqrt(2DS/H) * sqrt(p/p-u) = sqrt(2*6000*100/6) * sqrt(50/50-30) =707.106tons = 707.106*2000/100 bags =14142 bags
b)Imax = Q/p* (p-u)= 707.106/50* 20 =282.84 = 282.84
average = Imax /2 = 282.84/2= 141.42 = 141.42 * 2000/100 bags =2828 bags
c) runlength = q/p = 707.106/50 =14.14 days
d)runsper year = D/Q = 6000/707.106 =8.485
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