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In the process of producing 1 hormone-free, stress-free, happy cow, the New Age Cattle Ranch produces 1 ton of natural, organic plant fertilizer. Demand for the ranch’s cattle is given by Pc ? 2,000 − 5Qc, and demand for fertilizer is given by Pf ? 500 − 2Qf. The cost of producing Q cow-fertilizer bundles is C ? 5,000 ? 200Q. To maximize profits, the ranch should
a.produce 164.29 cow-fertilizer units, sell 164.29 cattle, and sell 164.29 tons of fertilizer.
b.produce 180 cow-fertilizer units, sell 180 cattle, and sell 125 tons of fertilizer.
c.produce 180 cow-fertilizer units, sell 180 cattle, and sell 75 tons of fertilizer.
d.produce 180 cow-fertilizer units, sell 180 cattle, and sell 180 tons of fertilizer.
e.produce 200 cow-fertilizer units, sell 200 cattle, and dispose of all the fertilizer in an environmentally friendly manner.
28.For each carload of ore removed from the Matchless Mine, 1 pound of lead and 1 ounce of silver is smelted. The cost of mining and processing 1 carload of ore is C(Q) ? 400 ? 2Q ? 0.04Q2. The demand for silver (per ounce) is Ps ? 30 − 0.30Qs and the demand for lead (per pound) is Pl ? 6 − 0.02Ql. What should the owners of the Matchless Mine do to maximize profits (in the long run)?
a.Mine and process 47.22 carloads of ore, sell 47.22 ounces of silver, and sell 47.22 pounds of lead.
b.Mine and process 50 carloads of ore, sell 50 ounces of silver, and sell 33.33 pounds of lead.
c.Mine and process 150 carloads of ore, sell 41.18 ounces of silver, and sell 150 pounds of lead.
d.Mine and process 150 carloads of ore, sell 50 ounces of silver, and sell 150 pounds of lead.
e.Shut down the mine.
29.For each carload of ore removed from the Matchless Mine, 1 pound of lead and 1 ounce of silver is smelted. The cost of mining and processing 1 carload of ore is C(Q) ? 300 ? 3Q ? 0.02Q2. The demand for silver (per ounce) is Ps ? 30 − 0.10Qs and the demand for lead (per pound) is Pl ? 6 − 0.03Ql. What should the owners of the Matchless Mine do to maximize profits (in the long run)?
a.Mine and process 150 carloads of ore, sell 150 ounces of silver, and sell 30 pounds of lead.
b.Mine and process 150 carloads of ore, sell 150 ounces of silver, and sell 100 pounds of lead.
c.Mine and process 110 carloads of ore, sell 110 ounces of silver, and sell 110 pounds of lead.
d.Mine and process 112.50 carloads of ore, sell 112.50 ounces of silver, and sell 100 pounds of lead.
e.Shut down the mine.
30.For each carload of ore removed from the Matchless Mine, 1 pound of lead and 1 ounce of silver is smelted. The cost of mining and processing 1 carload of ore is C(Q) ? 700 ? 2Q ? 0.09Q2. The demand for silver (per ounce) is Ps ? 40 − 0.30Qs and the demand for lead (per pound) is Pl ? 5 − 0.02Ql. What should the owners of the Matchless Mine do to maximize profits (in the long run)?
a.Mine and process 52.44 carloads of ore, sell 52.44 ounces of silver, and sell 52.44 pounds of lead.
b.Mine and process 66.67 carloads of ore, sell 66.67 ounces of silver, and sell 13.64 pounds of lead.
c.Mine and process 125 carloads of ore, sell 66.67 ounces of silver, and sell 125 pounds of lead.
d.Mine and process 125 carloads of ore, sell 48.72 ounces of silver, and sell 125 pounds of lead.
e.Shut down the mine.
PROBLEM
1.On a certain small island, there are 100 units of labor and 200 units of capital. Two goods can be produced. Good A is produced with fixed coefficients, using 1 unit of labor and 3 units of capital per unit of output. Good B is produced with fixed coefficients, using 1 unit of labor and 1 unit of capital per unit of output. Let X a denote the quantity of good A and X b be the quantity of good B that is produced. The set of feasible output combinations for this economy is restricted by the fact that it cannot use more than 100 units of labor or 200 units of capital.
a.Write down two inequalities expressed in terms of X a and X b that must be satisfied at feasible output combinations.
b.Draw a graph showing the economy’s production possibility set. Put numerical labels on your graph so that this graph is precisely described.
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