Consumer Surplus and Producer Surplus In Exercises 59-62, (a) graph the systems of inequalities representing the consumer surplus and producer surplus for the supply and demand equations and (b) find the consumer surplus and producer surplus.
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- Break-Even Analysis In Exercises 55 and 56, use the equations for the total cost C and total revenue R to find the number x of units a company must sell to break even. (Round to the nearest whole unit.) C=8650+250,000,R=9502xarrow_forwardRedo Exercise 5, assuming that the house blend contains 300 grams of Colombian beans, 50 grams of Kenyan beans, and 150 grams of French roast beans and the gourmet blend contains 100 grams of Colombian beans, 350 grams of Kenyan beans, and 50 grams of French roast beans. This time the merchant has on hand 30 kilograms of Colombian beans, 15 kilograms of Kenyan beans, and 15 kilograms of French roast beans. Suppose one bag of the house blend produces a profit of $0.50, one bag of the special blend produces a profit of $1.50, and one bag of the gourmet blend produces a profit of $2.00. How many bags of each type should the merchant prepare if he wants to use up all of the beans and maximize his profit? What is the maximum profit?arrow_forwardSystem of Linear Equations. In Exercises 57-62, use a software program or a graphing utility to solve the system of linear equations. 123.5x+61.3y32.4z=262.7454.7x45.6y+98.2z=197.442.4x89.3y+12.9z=33.66arrow_forward
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- A cleaning company charges $100 for each office it cleans. The fixed monthly cost of $480 for the company includes telephone service and the depreciation on cleaning equipment and a van. The variable cost is $60 per office and includes labor, gasoline, and cleaning supplies. (a) Write a linear cost function representing the cost C (x) (in $) to clean x offices per month. (b) Write a linear revenue function representing the revenue R (x) (in $) for cleaning x offices per month. (c) Determine the number of offices to be cleaned per month for the company to break even. (d) If 10 offices are cleaned, will the company make money or lose money?arrow_forwardAn athlete is planning a diet change for training. Each time he eats meal A he gets 20 grams of protein and 30 grams of carbohydrates. Each meal B provides 20 grams of protein and 50 grams of carbohydrates. Each meal A costs $5 each and each meal B costs $7.5. The athlete needs at least 80 grams of protein and 160 grams of carbohydrates. (A) let x be the number of meal A and y be the number of meal B. write inequalities for this linear programming problem. (B) identify the feasible set (C) Minimize the objective function 5x+7.5y (the total cost)arrow_forwardThe demand for wooden chairs can be modeled as D(p) = -0.01p + 4.25 million chairs where p is the price (in dollars) of a chair. (a) According to the model, at what price will consumers no longer purchase chairs? $ per chair Is this price guaranteed to be the highest price any consumer will pay for a wooden chair? Explain. According to the model, consumers ? ✓ purchase chairs at prices of $ (b) What quantity of wooden chairs will consumers purchase when the market price is $89.95? (Round your answer to three decimal places.) million chairs (c) Calculate the market price at which 3 million wooden chairs are in demand. $ per chair or higher. Since a demand schedule is a model of aggregate behavior, it ? (d) Calculate the consumers' surplus when consumers purchase 3 million wooden chairs. $ million guarantee individual behavior.arrow_forward
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