FM Corporation is a company that manufactures face masks. For every x thousand pieces of face mask sold, the company’s revenue (in thousand pesos) is R(x) = x(5 + x), x ≥ 0. If the company sold x thousand pieces of face mask, find the company’s marginal revenue.
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FM Corporation is a company that manufactures face masks. For every x thousand pieces of face mask sold, the company’s revenue (in thousand pesos) is R(x) = x(5 + x), x ≥ 0.
If the company sold x thousand pieces of face mask, find the company’s marginal revenue.
Note: Marginal revenue is the increase in revenue that results from the sale of one additional unit of output.
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- After an analysis of a large number of small businesses with two to nine employees, it was determined that, in a certain market sector, the operating costs C, in thousands of dollars, could be modeled by the function(pic#2)...., where p is the number of employees working for the firm. On the other hand, the realized revenue, R, of a firm could be determined as a function of the operating costs C, where R=(pic#1)... R and C are expressed in thousands of dollars. a) Based on the analysis, what would be the operating costs for a business with three employees? b) What would be the revenue for a company with three employees? c) Determine the equation that would model the realized revenue, R, as a function of the number of employees.You are an assistant to a senator who chairs an ad hoc committee on reforming taxes on telecommunication services. Based on your research, AT&T has spent over $15 million on related paperwork and compliance costs. Moreover, depending on the locale, telecom taxes can amount to as much as 25 percent of a consumer’s phone bill. These high tax rates on telecom services have become quite controversial, due to the fact that the deregulation of the telecom industry has led to a highly competitive market. Your best estimates indicate that, based on current tax rates, the monthly market demand for telecommunication services is given by Qd = 300 − 4P and the market supply (including taxes) is Qs = 3P − 120 (both in millions), where P is the monthly price of telecommunication services. The senator is considering tax reform that would dramatically cut tax rates, leading to a supply function under the new tax policy of Qs = 3.2P − 120. How much money per unit would a typical consumer save each…You are an assistant to a senator who chairs an ad hoc committee on reforming taxes on telecommunication services. Based on your research, AT&T has spent over $15 million on related paperwork and compliance costs. Moreover, depending on the locale, telecom taxes can amount to as much as 25 percent of a consumer’s phone bill. These high tax rates on telecom services have become quite controversial, due to the fact that the deregulation of the telecom industry has led to a highly competitive market. Your best estimates indicate that, based on current tax rates, the monthly market demand for telecommunication services is given by Qd = 300 - 4P and the market supply (including taxes) is QS = 3P - 120 (both in millions), where P is the monthly price of the telecommunication services.The senator is considering tax reform that would dramatically cut tax rates, leading to a supply function under the new tax policy of QS = 3.3P - 120. How much money per unit would a typical consumer save…
- You are an assistant to a senator who chairs an ad hoc committee on reforming taxes on telecommunication services. Based on your research, AT&T has spent over $15 million on related paperwork and compliance costs. Moreover, depending on the locale, telecom taxes can amount to as much as 25 percent of a consumer’s phone bill. These high tax rates on telecom services have become quite controversial, due to the fact that the deregulation of the telecom industry has led to a highly competitive market. Your best estimates indicate that, based on current tax rates, the monthly market demand for telecommunication services is given by Qd = 250 − 5P and the market supply (including taxes) is QS = 4P − 110 (both in millions), where P is the monthly price of the telecommunication services.The senator is considering tax reform that would dramatically cut tax rates, leading to a supply function under the new tax policy of QS = 4.171P − 110. How much money per unit would a typical consumer save…Making dresses is a labor-intensive process. Indeed, the production function of a dressmaking firm is well described by the equation Q = L − L2∕800, where Q denotes the number of dresses per week and L is the number of labor hours per week. The firm’s additional cost of hiring an extra hour of labor is about $20 per hour (wage plus fringe benefits). The firm faces the fixed selling price, P = $40. Over the next two years, labor costs are expected to be unchanged, but dress prices are expected to increase to $50. What effect will this have on the firm’s optimal output? A- Increase B- Decrease C- No EffectThe manager of a large apartment complex knows from experience that 100 units will be occupied if the rent is 414 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 9 dollar increase in rent. Similarly, one additional unit will be occupied for each 9 dollar decrease in rent. What rent should the manager charge to maximize revenue?
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- You are the manager of a local sporting goods store and recently purchased a shipment of 60 sets of skis and ski bindings at a total cost of $25,000 (your wholesale supplier would not let you purchase the skis and bindings separately, nor would it let you purchase fewer than 60 sets). The community in which your store is located consists of many different types of skiers, ranging from advanced to beginners. From experience, you know that different skiers value skis and bindings differently. However, you cannot profitably price discriminate because you cannot prevent resale. There are about 20 advanced skiers who value skis at $400 and ski bindings at $275; 20 intermediate skiers who value skis at $300 and ski bindings at $400; and 20 beginning skiers who value skis at $200 and ski bindings at $350. Determine your optimal pricing strategy.Market research for a certain ice cream company indicates that if the price per cup of ice cream is P50.00, the demand will be 1200 cups, whereas if the price is increased to P60.00, the demand will be 1100 cups. Therefore, at a production level of 200 cups of ice cream, the revenue generated by the company would be $130 for each additional cup of ice cream produced. Now, suppose it is known that the total cost of production of x cups of ice cream is given by C(x) = 3x + 25,500. (a) Find the value(s) of x at the break-even points. (b) Use marginal analysis to approximate the profit from the sale of the 500th cup of ice cream. Compare this value with the exact profit from the sale of the 500th cup.As the manager of Smith Construction, you need to make a decision on the number of homes to build in a new residential area where you are the only builder. Unfortunately, you must build the homes before you learn how strong demand is for homes in this large neighborhood. There is a 60 percent chance of low demand and a 40 percent chance of high demand. The corresponding (inverse) demand functions for these two scenarios are P = 400,000 −400Q and P = 900,000 −250Q, respectively. Your cost function is C(Q) = 125,000 + 430,000Q. How many new homes should you build, and what profits can you expect? Number of homes you should build: homes Profits you can expect: $