891 9.1 Systems of Linear Equations 111. Blending Coffee Beans Three varieties of coffee—Arabian Mocha Sanani, Organic Shade Grown Mexico, and Guatemala Antigua—are combined and roasted, yielding a 50-lb batch of coffee beans. Twice as many pounds of Guatemala Antigua, which retails for $10.19 per lb, are needed as of Arabian Mocha Sanani, which retails for $15.99 per lb. Organic Shade Grown Mexico retails for $12.99 per lb. How many pounds, to the nearest hundredth, of each coffee should be used in a blend that sells for $12.37 per lb? 112. Blending Coffee Beans Rework Exercise 111 if Guatemala Antigua retails for $12.49 per lb instead of $10.19 per lb. Does the answer seem reasonable? Relating Concepts For individual or collaborative investigation (Exercises 113–118) Supply and Demand In many applications of economics, as the price of an item goes up, demand for the item goes down and supply of the item goes up. The price where supply and demand are equal is the equilibrium price, and the resulting supply or demand is the equilibrium supply or equilibrium demand. Suppose the supply of a product is related to its price by the equation p = 2 3 q, where p is in dollars and q is supply in appropriate units. (Here, q stands for quantity.) Furthermore, suppose demand and price for the same product are related by p = - 1 3 q + 18, where p is price and q is demand. The system formed by these two equations has solution 118, 122, as seen in the graph. Use this information to work Exercises 113–118 in order. 113. Suppose the demand and price for a certain model of electric can opener are related by p = 16 - 5 4 q, where p is price, in dollars, and q is demand, in appropriate units. Find the price when the demand is at each level. (a) 0 units (b) 4 units (c) 8 units 114. Find the demand for the electric can opener at each price. (a) $6 (b) $11 (c) $16 115. Graph p = 16 - 5 4 q. 116. Suppose the price and supply of the can opener are related by p = 3 4 q, where q represents the supply and p the price. Find the supply at each price. (a) $0 (b) $10 (c) $20 117. Graph p = 3 4 q on the same axes used for Exercise 115. 118. Use the result of Exercise 117 to find the equilibrium price and the equilibrium demand. (18, 12) Equilibrium point 18 9 q 0 9 18 p p = q p = – q + 18 1 3 2 3
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