4. A number of inputs are required for producing corn. To simplify the problem, the production function for corn (bushels per acre) is given below, where x1 is all other inputs and x2 is pesticides. 0.5 0.25 V - X1 X2 a. If the price of corn is $3/bushel, r1 = $0.22 per unit, and r2 = $1.00 per pound, what are the profit maximizing levels of inputs and how much corn is produced? b. A local microbrewery uses groundwater to produce beer. The brewery claims that pesticides from the corn farm are contaminating the groundwater. Suppose the government, in an attempt to reduce the amount of pesticides used in corn production, placed a $0.10 per pound tax on pesticides that is added directly to the cost of pesticides. Estimate and discuss how the tax changes the cost minimizing combination of inputs used for corn production and demonstrate your results graphically. c. How much tax revenue would be raised if there were 500 corn growers affected by the tax? (Include any assumptions you need to make in your discussion.) d. Explain (graphically and with text) how the increase in ethanol production from corn influences the price of corn. e. If the price of corn increased to $10/bushel, the cost of pesticides $1.15/lb and all other inputs cost $5.00 per unit, what are the profit maximizing levels of inputs (both) to use