The demand and supply equations for an MP3 player are given by p = 123 - 11x p = 72 + 6x Demand equation Supply equation where p is the price (in dollars) and x represents the number of units (in hundreds of thousands). Find the equilibrium point for this market. (x, p) =
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- Write a uniform motion problem similar to Example 4.15 that relates to where you live with your friends or family members. Then translate to a system of equations and solve it.The demand equation for the Cold Spot compact refrigerator is 3x + 9p − 2520 = 0, where x is the quantity demanded each week and p is the unit price in dollars. The supply equation for these refrigerators is 2x − 55p + 3200 = 0, where x is the quantity the supplier will make available in the market when the wholesale price is p dollars each. Find the equilibrium quantity and the equilibrium price for the Cold Spot compact refrigerators.The quantity demanded of a certain model of a VCR is 8000 units when the unit price is $260. As the unit price decreases by $3, the number of VCRs demanded increases by 100 units. The manufacturer will not market any VCRs if the price is $100 or lower. However, for each $50 increase in the unit price above $100, the manufacturer will market an additional 1000 units. Demand: (8000, 260), (8100, 257) Provide the equations for the linear demand and supply functions: Also, define the variables. D(x) is the price the consumer is willing to spend when purchasing x number of VCRs. S(x) is the price the manufacture is willing to sell x number of VCRs Answer: D(x) = (-3/100)X + 500 and S(x) = (5/100)X + 100
- The Organization for Economic Cooperation and Development (OECD) consists of 20 industrialized countries. For these nations, the prediction equation relating y = child poverty rate (in percentage points) to x = social expenditure as a percentage of gross domestic product (GDP) is = 22-1.3x. In 2000, the actual child poverty rate ranged from 2.8% (in Finland) to 21.9% (in the U.S.). Social expenditure as a percentage of GDP ranged from 2% (in the United States) to 16% (in Denmark). What is the residual for the United States? You can use the information on the actual y-value given in the description of the study as well as information from your response to Question 3 to calculate this. Residual for the U.S. =The demand and supply functions for a certain brand of breath mints aredemand (?) = −20? + 150 and supply (?) = 80? − 50, where ? is the price indollars. When the breath mint market is in equilibrium, how many breathmints are bought and sold?The cost per unit of producing a product is 280 + 0.2x dollars, where x represents the number of units produced per week. If the equilibrium price determined by a competitive market is $420, how many units should the firm produce and sell each week to maximize its profit? unit
- A desk lamp factory is willing to supply x lamps for a price, in dollars, of p(x) = 6x + 193, while consumers are willing to buy x lamps at a price, in dollars, of p(x) = −3x + 328. Determine the market equilibrium point. (x, y) =Suppose that a company has determined that the demand equation for its product is 5x + 3p - 30 = 0 where p is the price of the product in dollars when x of the product are demanded (x is given in thousands). The supply equation is given by 52x - 30 p + 45 = 0, where x is the number of units that the company will make available in the marketplace at p dollars per unit. Find the equilibrium quantity and price.If the demand equation for an item is D(x)= -5x+ 80 and a supplier is willing to supply 10 items at $300 per item or 50 items at $1900 per item find equilibrium equilibrium quantity assuming linear supply and demand models
- The demand and supply functions for Pop's Pogo Sticks are given by 7x + 3p - 450 = 0 and 6x-2p-20=0 respectively, where p is the price in dollars, and x is the number of pogo sticks. Find the equilibrium price and quantity.The demand equation for the BWS Bluetooth wireless loudspeaker is p = −0.03x + 210 where x is the quantity demanded per month and p is the unit price in dollars. The corresponding supply equation is given by p = 0.015x + 30 where x is the quantity demanded per month and p is the unit price in dollars. Find the equilibrium quantity and the equilibrium price for the BWS Bluetooth wireless loudspeakers. equilibrium quantity units equilibrium price $A manufacturing process has a total cost function given by the equation C = 10 + 4x and a total revenue function given by the equation R = 22x - 4x2 where x is the quantity produced in ’00 units and C and R , are both N$’00. i. Using the cost equation, C = 10 + 4x, identify the value of the company’s fixedcosts (i.e. those that remain constant irrespective of the quantity produced) andvariable costs (i.e. those that vary according to production) for thismanufacturing process. ii. Construct a table to calculate the value of C and R using the values 0, 1, 2, 3, 4and 5 for x. iii. (Using the data from the table in (ii), plot a fully labelled graph for C and Ragainst x. Use the graph drawn in (iii) to determine:iv. The quantity of units produced where the manufacturing process breaks even(i.e. where neither a profit nor a loss is made). v. The range of x in which the manufacturing process makes a profit and the rangein which the manufacturing process makes a loss. vi. The profit or loss…