S(x) = -x3 + 6×2 + 288x + 4000, 4 ≤ x ≤ 20 is an approximati…
S(x) = -x3 + 6×2 + 288x + 4000, 4 ≤ x ≤ 20 is an approximation to the number of salmon swimming upstream to spawn, where x represents the water temperature in degrees Celsius. Find the temperature that produces the maximum number of salmon.
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Answer Format: Do not enter $ sign nor decimals. Each answer will be a whole number. An office supply company sells x mechanical pencils per year at $p per pencil. The price equation for these pencils is p=10 – 0.001x. Determine the revenue function (R=xp) and use it along with its derivative to find: a) how many pencils must be sold in order to maximize revenue. x=[BLANK-1] b) the maximum revenue. R = $ [BLANK-2] c) the price (p) that yields maximum revenue. p = $ [BLANK-3] Furthermore, suppose cost is C(x)=5000 + 2x. Use this and the above information to answer the following. d) how many pencils must be sold to maximize profit (P=R-C)? x=[BLANK-4] e) find the maximum profit. P = $ [BLANK-5]
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