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Math for Econ I- Practice ProblemsNew York University1. Supply and demand1. In a California town, the monthly charge for waste collection is $8 for 32 gallons of waste and $12.32 for 68 gallonsof waste.(a) Find a linear formula for the cost,C, of waste collection as a function of the number of gallons of waste,w.(b) What is the slope of the line found in part (a)? Give units and interpret your answer in terms of the costof waste collection.(c) What is the vertical intercept of the line found in part (a)? Give units and interpret your answer in termsof the cost of waste collection.Solution:
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2. Production costs for manufacturing running shoes consist of a fixed overhead of $650,000 (“fixed cost”) plus acost of $20 per pair of shoes (“variable cost”). Each pair of shoes sells for $70.(a) Find the total cost,C(q), the total revenue,R(q), and the total profit,⇡(q), as a function of the number ofpairs of shoes produced,q.(b) How many pairs of shoes must be produced and sold for the company to make a profit?Solution: