The demand equation for handcrafted violins by a certain violin maker can be approximated by p=20-x where p is the price in thousands of dollars and x is the quantity of violins demanded. Find and interpret the marginal revenue for each of the given production levels. (a) x = 7 (b) x = 10 (c) x = 11

Worldwide annual sales on smart phones over a two year period were approximately q=-5p+3090 million phones at the selling price of $p per phone. (a) obtain a formula for the price elasticity of demand E. E=______ (b) in one of the years the actual selling price was $355 per phone. What was the corresponding price elasticity of demand? E=______ The demand is going (up/down) by about _____% per 1% increase in that price level.

A large company in the communication and publishing industry hs quantified the relationship between the price of one of its products and the demand for this product as Price = 160 -0.01 xDemand for an annual printing of this particular product. The foxed costs per year (ie. per printing) = $4T 000 and the variable cost per unit = $35. What is the maximum profit that can be achieved? What is the unit price at this point of optimal demand? Demand is not expected to be more than 7,000 units per year. The maximum profit that can be achieved is S. (Round to the nearest dolar.) The unit price at the point of optimal demand is S per unit (Round to the nearest cent)

Consider the market for good x for which there is one firm controlling the market.D(q)=165-10qMC(q)=5q+15MR(q)=165-20qC(q)=2.5q^2+15q+8 (a) Find the point of equilibrium. (b) How many units must the firm produce and sell to maximize its profits? (c) What will be the price the firm will charge to consumers?