Exam 31: Production

Tip can write 2 pages of term paper or solve 2 workbook problems in an hour, while Spot can write 2 pages of term paper or solve 6 workbook problems in an hour. If they each decide to work a total of 8 hours and to share their output, then if they produce as many pages of term paper as possible given that they produce 14 workbook problems,

Al and Bill are the only workers in a small factory which makes geegaws and doodads. Al can make 5 geegaws per hour or 15 doodads per hour. Bill can make 2 geegaws per hour or 12 doodads per hour. Assuming that neither of them finds one task more odious than the other,

A small company produces two goods, swords and plowshares. The company has 100 type alpha employees and 100 type beta employees. If an alpha devotes all his time to producing swords, he can make 2 swords per week. If he devotes all his time to producing plowshares, he can make 4 plowshares per week. A beta can produce either 1 plowshare per week or 1 sword per week. The company wants to produce 218 swords and as many plowshares as it can. How many type betas should it employ at making swords?

Al and Bill are the only workers in a small factory which makes geegaws and doodads. Al can make 5 geegaws per hour or 15 doodads per hour. Bill can make 4 geegaws per hour or 8 doodads per hour. Assuming that neither of them finds one task more odious than the other,

On a certain island there are only two goods, wheat and milk. The only scarce resource is land. There are 1,000 acres of land. An acre of land will produce either 14 units of milk or 15 units of wheat. Some citizens have lots of land; some have just a little bit. The citizens of the island all have utility functions of the form U(M, W) = MW. At every Pareto optimal allocation,

Amy Canvas is an artist who produces sketches and paintings. She can produce 12 sketches a week if she spends all of her workday sketching. She can produce 3 paintings a week if she spends all of her workdays painting. The rate at which she produces either sketches or paintings is independent of how many she makes. She can divide her time in any way she wishes between sketching and painting. If you draw her production possibilities frontier with sketches on the horizontal axis and paintings on the vertical axis, the production possibilities frontier will be

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 P_s = 40 - 0.30Q_s and the demand for lead (per pound) is P_l = 5 - 0.02Q_l. What should the owners of the Matchless Mine do to maximize profits (in the long run)?

Tip can write 2 pages of term paper or solve 4 workbook problems in an hour, while Spot can write 4 pages of term paper or solve 12 workbook problems in an hour. If they each decide to work a total of 6 hours and to share their output, then if they produce as many pages of term paper as possible given that they produce 10 workbook problems,

A small company produces two goods, swords and plowshares. The company has 100 type alpha employees and 100 type beta employees. If an alpha devotes all his time to producing swords, he can make 3 swords per week. If he devotes all his time to producing plowshares, he can make 6 plowshares per week. A beta can produce either 1 plowshare per week or 1 sword per week. The company wants to produce 324 swords and as many plowshares as it can. How many type betas should it employ at making swords?

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 P_c = 2,000 - 5Q_c, and demand for fertilizer is given by P_f = 500 - 4Q_f. The cost of producing Q cow-fertilizer bundles is C = 5,000 + 400Q. To maximize profits, the ranch should

On a certain island there are only two goods, wheat and milk. The only scarce resource is land. There are 1,000 acres of land. An acre of land will produce either 8 units of milk or 15 units of wheat. Some citizens have lots of land; some have just a little bit. The citizens of the island all have utility functions of the form U(M, W) = MW. At every Pareto optimal allocation,

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 P_c = 2,000 - 5Q_c, and demand for fertilizer is given by P_f = 500 - 2Q_f. The cost of producing Q cow-fertilizer bundles is C = 5,000 + 200Q. To maximize profits, the ranch should

Ernie and Burt both make pizzas for a living. Making a pizza consists of two tasks: making the crust and applying toppings. Ernie can make crusts at the rate of 30 crusts per hour. He can apply toppings at the rate of 15 toppings per hour. Burt can make crusts at the rate of 15 crusts per hour. He can apply toppings at the rate of 30 toppings per hour. After years of operating separate, one-man shops, they realize they can produce more efficiently by combining operations and dividing the tasks between them. How many more pizzas per hour can they make if they work together and allocate tasks efficiently than they made when they worked separately?

Robinson Crusoe's preferences over coconut consumption, C, and leisure, R, are represented by the utility function U(C, R) = CR. There are 48 hours available for Robinson to allocate between labor and leisure. If he works L hours, he will produce the square root of L of coconuts. He will choose to work

Al and Bill are the only workers in a small factory which makes geegaws and doodads. Al can make 4 geegaws per hour or 12 doodads per hour. Bill can make 2 geegaws per hour or 8 doodads per hour. Assuming that neither of them finds one task more odious than the other,