A factory produces a mixture of peanuts and cashews. The company guarantees that at least 30% of the total weight is cashews. The factory has a contract to produce at least 1000 pounds of the mixture. The peanuts cost $0.90 per pound, and the cashews cost $1.60 per pound to produce. Find the amount of each kind of nut the company should use to minimize the cost if 700 pounds of peanuts are available. What is the minimized cost? You can use decimals and/or fractions for this problem. Define the variables. State the objective. Write the objective function. Write the constraints. Use the method of corners to solve, show work. Label your lines and mark the feasible region with an S. Interpret the solution with context to the application. Don’t forget units.
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.
For Problems 1-5:
A factory produces a mixture of peanuts and cashews. The company guarantees that at least 30% of the total weight is cashews. The factory has a contract to produce at least 1000 pounds of the mixture. The peanuts cost $0.90 per pound, and the cashews cost $1.60 per pound to produce. Find the amount of each kind of nut the company should use to minimize the cost if 700 pounds of peanuts are available. What is the minimized cost? You can use decimals and/or fractions for this problem.
- Define the variables.
State the objective.
Write the objective function.- Write the constraints.
- Use the method of corners to solve, show work. Label your lines and mark the feasible region with an S. Interpret the solution with context to the application. Don’t forget units.
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