Assignment 5 - Calculus etc. - Assignment 5 Problems...

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Assignment 5 – Problems involving calculus 1. A North Carolina farmer is raising pigs. Each day her average pig adds 5 pounds per day. Today the average pig weighs 200 pounds. The current price per pound is $0.65 however the price seems to be decreasing by a cent per pound per day. It costs the farmer an average of $0.45 per day per pig. When should the farmer sell her ‘average’ pigs so as to maximize her net income? a) Construct a model and solve using Lingo or similar program. b) Solve by calculus. ( Find the derivative of the net income function with respect to what is unknown (time) and set to 0. Then solve for time. ) 2. The municipalities bordering on Lake Cayuga are concerned about the amount of phosphorus entering the Lake, and its accompanying weed and algae growth. One major polluter is a chicken farm. In order to create an incentive for the chicken farmer to reduce its phosphorus load into the lake it is considering a tax. There are two options: A flat tax imposed until the load is reduced to some specified maximum amount, or a tax per unit of phosphorus discharged. Which option is best and how much should the tax be? What data do you need to address this issue? What are the unknown variables that you want to solve for? Construct a general model that can be used to estimate the impact of a tax on meeting the effluent requirements. Sketch graphically the impact of a tax on the income of and cost to the farm, on the
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Assignment 5 - Calculus etc. - Assignment 5 Problems...

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