23. Embassy Motorcycles manufacturers two lightweight motorcycles designed for easy handling and safety. The EZ-Rider model has a new engine and a low profile that make it easy to balance. The Lady-Sport model is slightly larger, uses a more traditional engine, and is specifically designed to appeal to women riders, Embassy produces the engines for both models at its Des Moines, Iowa plant. Each EZ-Rider engine requires 6 hours manufacturing time and Lady-Sport requires 3 hours manufacturing time. The Des Moines plant has 2100 hours of engine manufacturing time available for the next production period. Embassy’s motorcycle frame supplier can supply as many EZ-Rider frames as needed. However, the Lady-Sport frame is more complex, and the supplier can only provide up to 280 Lady-Sport frames for the next production period. Final assembly and testing require 2 hours for each EZ-Rider model and 2.5 hours for each Lady-Sport model. A maximum or 1000 hours of assembly and testing time are available for the next production period. The company’s accounting department projects a profit contribution of $2400 for each EZ-Rider produced and $1800 for each Lady-Sport produced. a. What is the optimal solution value for E (number of units of the EZ-Rider)?b. What is the optimal solution value for L (number of units of the Lady-Sport)?c. What is the profit?
Addition Rule of Probability
It simply refers to the likelihood of an event taking place whenever the occurrence of an event is uncertain. The probability of a single event can be calculated by dividing the number of successful trials of that event by the total number of trials.
Expected Value
When a large number of trials are performed for any random variable ‘X’, the predicted result is most likely the mean of all the outcomes for the random variable and it is known as expected value also known as expectation. The expected value, also known as the expectation, is denoted by: E(X).
Probability Distributions
Understanding probability is necessary to know the probability distributions. In statistics, probability is how the uncertainty of an event is measured. This event can be anything. The most common examples include tossing a coin, rolling a die, or choosing a card. Each of these events has multiple possibilities. Every such possibility is measured with the help of probability. To be more precise, the probability is used for calculating the occurrence of events that may or may not happen. Probability does not give sure results. Unless the probability of any event is 1, the different outcomes may or may not happen in real life, regardless of how less or how more their probability is.
Basic Probability
The simple definition of probability it is a chance of the occurrence of an event. It is defined in numerical form and the probability value is between 0 to 1. The probability value 0 indicates that there is no chance of that event occurring and the probability value 1 indicates that the event will occur. Sum of the probability value must be 1. The probability value is never a negative number. If it happens, then recheck the calculation.
23. Embassy Motorcycles manufacturers two lightweight motorcycles designed for easy handling and safety. The EZ-Rider model has a new engine and a low profile that make it easy to balance. The Lady-Sport model is slightly larger, uses a more traditional engine, and is specifically designed to appeal to women riders, Embassy produces the engines for both models at its Des Moines, Iowa plant. Each EZ-Rider engine requires 6 hours manufacturing time and Lady-Sport requires 3 hours manufacturing time. The Des Moines plant has 2100 hours of engine manufacturing time available for the next production period. Embassy’s motorcycle frame supplier can supply as many EZ-Rider frames as needed. However, the Lady-Sport frame is more complex, and the supplier can only provide up to 280 Lady-Sport frames for the next production period. Final assembly and testing require 2 hours for each EZ-Rider model and 2.5 hours for each Lady-Sport model. A maximum or 1000 hours of assembly and testing time are available for the next production period. The company’s accounting department projects a profit contribution of $2400 for each EZ-Rider produced and $1800 for each Lady-Sport produced.
a. What is the optimal solution value for E (number of units of the EZ-Rider)?
b. What is the optimal solution value for L (number of units of the Lady-Sport)?
c. What is the profit?
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Refer to the original question, but use this data instead:
use this data instead:
| Max 2500E + 2100L |
| s.t. |
| 6E+4L <= 2400 |
| L <= 250 |
| 3E + 4L <= 1500 |
| E,L >= 0 |
a. What is the optimal solution value for E (number of units of the EZ-Rider)?
b. What is the optimal solution value for L (number of units of the Lady-Sport)?
c. What is the profit?
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