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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
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- A municipal solid-waste site for a city must be located at Site A or Site B. After sorting, some of the solid refuse will be transported to an electric powerplant where it will be used as fuel. Data for the hauling of refuse from each site to the power plant are shown in Table P2-4. If the power plant will pay $8.00 per cubic yard of sorted solid waste delivered to the plant, where should the solid-waste site be located? Use the city’s viewpoint and assume that 200,000 cubic yards of refuse will be hauled to the plant for one year only. One site must be selected.Assuming an M/M/1 system setup with a service rate of 25 entities per hour and an idling ratioof 4% Define the system’s birth rate. Define at least two ways of arriving at the number of entities in the system. Define the ratio of the time an entity spends waiting and the time the entity spends in thesystem?Further to the information provided in the question above, we are informed that nails produced thatare shorter than the minimum acceptable length have to be scrapped. Consider that 4.8cm is still theminimum threshold for acceptable nail length. If the cost to produce one nail is 45 cents, how muchdoes the company incur in Rand losses due to scrapping?
- The Boeing Company faces a critical strategic choice in its competition with Airbus Industries for the long-haul flight segment: Should it design and build a super-747 model that can carry 550 passengers at speeds around 350 mph, or a plane that can fly at 95 percent of the speed of sound but carry only about 350 passengers? As a member of Boeing's Planning Group, your task is to build a model to investigate the trade-offs involved in this decision.In the process of producing engine valves, the valves are subjected to a first grind. Valves whose thicknesses are within the specification are ready for installation. Those valves whose thicknesses are above the specification are reground, while those whose thicknesses are below the specification are scrapped. Assume that after the first grind, 73% of the valves meet the specification, 21% are reground, and 6% are scrapped. Furthermore, assume that of those valves that are reground, 46% meet the specification, and 54% are scrapped. Given that a valve meets the specification, what is the probability that it was ground only once?2. Are the strengths of Alloy A more consistent than Alloy B?
- In the process of producing engine valves, the valves are subjected to a first grind. Valves whose thicknesses are within the specification are ready for installation. Those valves whose thicknesses are above the specification are reground, while those whose thicknesses are below the specification are scrapped. Assume that after the first grind, 70% of the valves meet the specification, 20% are reground, and 10% are scrapped. Furthermore, assume that of those valves that are reground, 90% meet the specification, and 10% are scrapped. a) Find the probability that a valve is ground only once. b) Given that a valve is not reground, what is the probability that it is scrapped? c) Find the probability that a valve is scrapped. d) Given that a valve is scrapped, what is the probability that it was ground twice? e) Find the probability that the valve meets the specification (after either the first or second grind). f) Given that a valve meets the specification (after either the first or…In the process of producing engine valves, the valves are subjected to a first grind. Valves whose thicknesses are within the specification are ready for installation. Those valves whose thicknesses are above the specification are reground, while those whose thicknesses are below the specification are scrapped. Assume that after the first grind, 74% of the valves meet the specification, 18% are reground, and 8% are scrapped. Furthermore, assume that of those valves that are reground, 88% meet the specification, and 12% are scrapped. Draw a tree diagram to represent the situation Find the probability that a valve is ground only once Given that a valve is not reground, what is the probability that it is scrapped? Find the probability that a valve is scrapped Given that a valve is scrapped, what is the probability that it was ground twice? Find the probability that the valve meets the specification (after either the first or second grind). Given that a valve meets the specification…1.Suppose that the weight of a type of organism is governed by a power law relationship with its length from snout to tail and the thickness of its central vertebrae
- The (partial) cost sheet for the single product manufactured at Briarcliff Corporation follows: Direct labor (2 hours @ $30) $ 60 Variable overhead (2 hours @ $9) 18 Fixed overhead (2 hours @ $11) 22 The master budget level of production is 45,570 direct labor-hours, which is also the production volume used to compute the fixed overhead application rate. Other information available for operations over the past accounting period include the following: Actual variable overhead incurred $ 582,000 Actual fixed overhead incurred 480,100 Direct labor efficiency variance 80,100 F Variable overhead price variance 142,800 U Required:a. What was the variable overhead efficiency variance?b. What was the fixed overhead price variance?c. What was the fixed overhead production volume variance?Explain the Stationarity in the AR(1) Model?The management of BCD Inc. would like to separate the fixed and variable components of electricity as measured against machine hours in one of its plants. Data collected over the most recent six months follow:Electricity MachineMonth Cost Hours January $1,100 4,500February 1,110 4,700March 1,050 4,100April 1,200 5,000May 1,060 4,000June 1,120 4,600Required: 1. Using the method of least squares, compute the fixed cost and the variable cost rate for electricity expense. (Round estimates to the nearest cent.) 2. Compute coefficients of correlation and determination