14. Suppose that the supply equation is p = S(q) = 3 + 16q, the equilibrium price is 67, and the or, an quantity demanded is 10 when the price is 49. Find the demand equation. Show the work above, and write your answer in the box below. 0 | = |(\ = 1) 3121.0
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- Suppose the inverse market demand function is P = 20 −Q and the total cost function is TC = Q2.1.1. If the market only has one firm, what would be the monopoly output and profit?1.2. If the market has two symmetric firms (each with the total cost function C = Q2), what is the Cournot equilibrium quantity and profit?1.3. If there are two symmetric firms as in 1.2, what level of output for each firm would maximize the total industry profit? Why is this total profit different than in 1.1? Suppose the two firms in 1.3 engage in Cournot competition for just one period. Show that the output levels in 1.3 are not sustainable in a collusion. Suppose the two firms in 1.3. engage in Cournot competition for infinitely many periods. What is the lowest discount factor δ that would sustain the output levels in 1.3 in a collusion using the grim trigger strategy?A certain company is interested in maximizing the monthly profit from two of its products, designated I and II. To manufacture these products the company uses a type of machine that has an availability of 200 machine-hours per month and a hand type of workforce with an availability of 240 man-hours per month. To produce a unit of product I, 5 machine hours and 10 labor hours are required, while for the product II, 4 hours of labor are used. Demand for 20 units is expected per month of product I and 45 units of product II. A profit per unit of US$ 10.00 is calculated for product I and US$ 6.00 for product II. Determine the quantities of each product which must be manufactured per month, for the maximum monthly profit.Assume that producing 1 unit of calcium requires 0.1 units of calcium, 0.2 units of hydrogen, and 0 units of sea salt; that producing 1 unit of hydrogen requires 0 units of calcium, 0 units of hydrogen, and 0 units of sea salt; and that producing 1 unit of sea salt requires 0.5 units of calcium, 0.2 units of hydrogen, and 0.1 units of sea salt.Find the production schedule that satisfies an external demand for 43 units of calcium, 38 units of hydrogen, and 19 units of sea salt.X=
- Assume that the production of 1 unit of magnesium requires 0.5 units of magnesium and 0.6 units of aluminum, and that the production of 1 unit of aluminum requires 0.5 units of magnesium and 0.2 units of aluminum.Find the production schedule that satisfies an external demand for 60 units of magnesium and 20 units of aluminum.Telefonika is a telecommunication company, located in the Accra Mall, selling mobile phones and accessories. Most of their new phones are ordered. But, Telefonika stocks three main phones for walk-in customers. Every week, they generate profit of GH¢600 from selling Galaxy S2, GH¢400 from Galaxy S3 and GH¢300 from Galaxy S4. The overall weekly cost of these types of phones are GH¢1,800, GH¢2,100 and GH¢1,200 respectively. This week, Telefonika has a budget of GH¢12,000 available to buy these three types of phones. During sales, each phone type must be unpacked, leading to 8 hours of unpacking time for S2 phones, 12 hours for S3 phones and 16 hours for S4 phones. The manager estimates that he and his workers have 120 labour hours available to unpack the three types of phones. Telefonika has enough space to order 20 phones this week. The manager also wants to stock at least twice as many S4 as S2 and S3 phones because S4 phones sell better.a) Formulate a linear programming model for this…Assume that the production of 1 unit of magnesium requires 0.6 units of magnesium and 0.2 units of aluminum, and that the production of 1 unit of aluminum requires 0.5 units of magnesium and 0.5 units of aluminum.Find the production schedule that satisfies an external demand for 60 units of magnesium and 40 units of aluminum. X=
- A chemical manufacturing plant can produce zz units of chemical Z given pp units of chemical P and rr units of chemical R, where: z=160p^0.9r^0.1 Chemical P costs $400 a unit and chemical R costs $2,400 a unit. The company wants to produce as many units of chemical Z as possible with a total budget of $1,440,000.A) How many units each chemical (P and R) should be "purchased" to maximize production of chemical Z subject to the budgetary constraint?Units of chemical P, p= Units of chemical R, r = B) What is the maximum number of units of chemical Z under the given budgetary conditions? (Round your answer to the nearest whole unit.)Max production, z= unitsconsidering marketing a new product with a four-year life. Epica will need to install new equipment to manufacture the product. Epica has to choose between two machines both of which would be suitable.Machine 1 costs K460,000 to purchase and install, and will have a residual value of K20,000 at the end of four years. Machine 2 costs K630,000 to purchase and install, and has a residual value of K30,000 at the end of four years. Machine 2 takes slightly longer to install and commission, but once in operation it has slightly lower operating costs per unit, and will eventually produce more output.The following projections have been prepared of the cash flows from product sales and operating costs for the two machines: Machine 1 Machine 2 Sales K’000 Costs K’000 Sales K’000 Costs K’000 Year…To minimize costs on the production line, an industrial engineer at a fiber-optic manufacturing firm is considering two robots. Robot X would have a $82,000 first cost, a $30,000 annual maintenance and operation (M&O) cost, and $50,000, $42,000, and $35,000 salvage prices after 1, 2, and 3 years, respectively. Robot Y will have a first cost of $97,000, a yearly M&O cost of $27,000, and after 1, 2, and 3 years, respectively, salvage prices of $60,000, $51,000, and $42,000. If a 2-year study period is specified at an interest rate of 15 percent per year and replacement after 1 year is not an option, what robot should be selected?
- Can I get help with this coordinatization problem?In the Erlang loss model, system A has 5 servers and an implied utilization of 125 percent,while system B has 15 servers and an implied utilization of 125 percent. Which of thefollowing statements is true?a. System A has the higher utilization because it has fewer servers relative to the potentialdemand.b. The two systems have the same utilization because they have the same implied utilization.c. System B has a higher utilization because the fraction of lost demand is lower in that system.d. More information is needed to determine which system has the higher utilization.