1) Producers will supply ???? units of a certain commodity to the market when the price is ???? = ????(????) dollars per unit, and the consumers will demand (buy) ???? units when the price is ???? = ????(????) dollars per unit where ????(????) = ???????? + ???? and ????(????) = ???????? + ???? for constants ????, ????, ???? and ????. Express the equilibrium production level and the equilibrium price in terms of the coefficients ????, ????, ???? and ????.

2) A manufacturer of a product sells all that is produced. The total revenue is given by ???????????? = 16????, and the total cost is given by ???????????? = 4???? + 14400, where ???? represents the number of units produced and sold. (a) Find the level of production at the break-even point, and draw the break-even chart. (b) Find the level of production at the break-even point if the total cost increases by 5%?

3) ???????????? = 0.5???? 2 + 12???? represents total revenue in dollars and ???????????? = 7???? + 352 represents total cost in dollars for a manufacturer. If ???? represents both the number of units produced and the number of units sold, find the break-even price.

4) A manufacturer of dining-room sets produced two styles: early American and contemporary. From past experience, management has determined that 22% more of the early American styles can be sold than the contemporary styles. A profit of $150 is made on each early American set sold, whereas a profit of $250 is made on each contemporary set. If, in the forthcoming year, management desires a total profit of $4060, how many units of each style must be sold?

5) Supply and demand equations for a certain product are 3???? − 200???? + 1800 = 0 and 3???? + 100???? − 1800 = 0 respectively, where p represents the price per unit in dollars and q represents the number of units sold per time period. (a) Find the equilibrium price algebraically, and show the system in the coordinate plane. (b) Find the equilibrium price when a tax of 27 cents per unit is imposed on the supplier.

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