Question

If $w$ pounds per acre of nitrogen fertilizer are spread on a corn field, the yield is $230 - 4300 / (w + 22)$ bushels of corn per acre. Corn sells for $4.25 per bushel, and fertilizer costs $0.50 per pound. All other costs of growing and harvesting the corn total $600 per acre and do not depend on the amount of fertilizer used. A) How much nitrogen fertilizer per acre should the farmer use to maximize his net dollar return per acre? lb/acre B) If the farmer uses the optimum amount of fertilizer, what will be his net dollar return per acre? $ per acre.

          If $w$ pounds per acre of nitrogen fertilizer are spread on a corn field, the yield is $230 - 4300 / (w + 22)$ bushels of corn per acre. Corn sells for $4.25 per bushel, and fertilizer costs $0.50 per pound. All other costs of growing and harvesting the corn total $600 per acre and do not depend on the amount of fertilizer used.

A) How much nitrogen fertilizer per acre should the farmer use to maximize his net dollar return per acre? lb/acre
B) If the farmer uses the optimum amount of fertilizer, what will be his net dollar return per acre? $ per acre.
        
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Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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If $w$ pounds per acre of nitrogen fertilizer are spread on a corn field, the yield is $230 - 4300 / (w + 22)$ bushels of corn per acre. Corn sells for $4.25 per bushel, and fertilizer costs $0.50 per pound. All other costs of growing and harvesting the corn total $600 per acre and do not depend on the amount of fertilizer used. A) How much nitrogen fertilizer per acre should the farmer use to maximize his net dollar return per acre? lb/acre B) If the farmer uses the optimum amount of fertilizer, what will be his net dollar return per acre? $ per acre.
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Transcript

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00:01 So the company's revenue function is r of x and the company's cost function is c of x and the company's profit function is p of x.
00:16 So to obtain the revenue function, multiply the output level by the price function.
00:23 So here, w pounds per acre of nitrogen fertilizers are spread on a cornfield and the yield is 230 minus 4 ,300 divided by w plus 22.
00:37 So corn sells at x is equals to $4 .25 per bushel.
00:50 And the fertilizer costs total corn...
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