5. Electron Control, Inc., a manufacturer of voltage regulators for industrial power generators, currently consolidates production at a single plant in Chattanooga, Tennessee, but a multiplant alternative to centralized production is being considered. Estimated demand, marginal revenue, and single-plant production cost curves for the firm are

P = 515 ? 0.005Q

MR = 515 ? 0.01Q

TC = 160,000 + 35Q + 0.01Q2

MC = 35 + 0.02Q

A) Find the single-plant profit-maximizing level of output.

B) Find the minimum efficient scale of the single-plant operation.

C) Assuming that multiple smaller plants production is possible under the same cost conditions described above, find the profit-maximizing multiplant level of output.

D) Given your answers to parts B and C, how many number of plants should you suggest?

6.6.6 Fish Plant Production Quantfisher Inc. buys fresh fish for processing. Quantfisher has an annual contract with its supplier to buy up to 4600 Tonnes at the following set of incremental prices: First 1000 Tonnes (or any fraction) may be purchased @ $0.80/kg. Next 2000 Tonnes (or any fraction) may be purchased @ $1.00/kg. Next 1600 Tonnes (or any fraction) may be purchased @ $1.20/kg. Quantfisher's fish processing plant can operate on a one, two, or three shift per day basis. (Shift two operates only if shift one operates, and shift three operates only if shift two operates.) For each shift there is a fixed cost which exists if the shift operates, but is nil otherwise, and a variable cost per kilogram of fish processed. The costs and shift capacities are: Fixed Cost Variable Cost Annual Capacity Shift Per Annum Per Kilogram (Tonnes) 1 $500,000 $0.50 1700 2 $300,000 $0.70 1500 3 $100,000 $0.95 1300 If a shift operates at all, then the minimum amount processed is 1000 Tonnes per annum on that shift (i.e. the amount processed on any shift is either 0 or greater than or equal to 1000 Tonnes). Quantfisher can sell processed fish for $1.80 per kg. They wish to know what they should do to maximize their annual profit. (a) Formulate this problem. (b) Solve it using the Excel Solver.To do The classical energy flow example Silver Springs, in central Florida is famous amongst ecologists as the place where Howard T. Odum researched energy flow in the ecosystem in the 1950s. Odum (1924-2002) was a pioneer ecologist working on ecological energetics. This was the first time an energy budget measurement was attempted when Odum measured primary productivity and losses by respiration. (Later, near the end of a long and illustrious career, he and David Scienceman developed the concept of emergy (embodied energy) which is a measure of the quality and type of energy and matter that go into making an organism.) Figure 2.3.14 shows the energy flows and biomass stores measured by Odum at Silver Springs. This simple community consists of algae and duckweed [producers); tadpoles, shrimps and insect larvae [herbivores); water beetles and frogs (first carnivores]; small fish (top consumers); and bacteria, bivalves and snails (decomposers and detritivores]. Dead leaves also fall into the water and spring water flows out, exporting some detritus