A rock company uses five types of rocks to fill four orders. The phosphate conte
ID: 2717297 • Letter: A
Question
A rock company uses five types of rocks to fill four orders. The phosphate content, availability of each type of rock, and the production cost per pound for each rock are listed below, as well as the size of each order and the minimum and maximum phosphate percentage in each order. What is the cheapest way to fill the orders? (Hint: this is a blending problem which will require you to constrain the weighted average)
Rock type Cost % phosphate Amount A $1.00 2.0% 500 B $5.00 5.0% 600 C $5.50 4.5% 700 D $2.00 3.0% 400 E $1.20 6.0% 450Explanation / Answer
Order 1 2 3 4 Total Min % phosphate 3.50% 3.80% 4% 3.60% Max % phosphate 4.40% 4.60% 4.70% 4.80% Order size 500 600 500 350 Cost per pound 3.28 3.28 3.28 3.28 Total cost 1639.62 1967.55 1639.62 1147.74 6394.53 Answer: $6,394.53 Phosphate Qty Total Cost A 2% 500 10 500 B 5% 600 30 3000 C 4.50% 700 31.5 3850 D 3% 400 12 800 E 6% 450 27 540 Total 2650 110.5 8690 Weighted Average % (110.5/2650) 4.17% Waitghted Cost (8690/2650) 3.28
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