6 part problem, short answers: 1.revenue function 2.revenue question 3.profit function 4. maximizing profit 5.break even 6.maximize profit

I wrote my problem in a "microsoft word" file. I attached it to this file. Thanks :)

matrix methods/solving equations

Protein, carbohydrates, and fats can be obtained from three foods. Each ounce of food I contains 5 grams of protein, 10 grams of carbohydrates, and 40 grams of fat. Each ounce of Food II contains 10 grams of protein, 5 grams of carbohydrates, and 30 grams of fat. Each ounce of Food III contains 15 grams of protein, 15 grams of carbohydrates, and 80 grams of fat. How many ounces of each of the three foods are required to yield 300 grams of protein, 300 grams of carbohydrates, and 1500 grams of fat? (o arrive at your conclusion, define variables, set up a system of equations, and solve it using matrix methods.)

profit functions/solving problems

Crystal Images is a manufacturer of collectible statues. The price per statue at which x statues can be sold in a month is given by p(x)= 655 - 10x dollars. The monthly cost of producing x statues is C(x) = 4800 + 100x dollars. Assume that 0<- x <- 50. (**the <- sign is the greater than or equals to sign, Im not sure how write it on the computer.**) Determine the number of statues that must be sold in order to have a profit of at least $2000. Show all supporting work (graphs, etc.).

Discrete Random Variables and Their Probability Functions - Poisson Distribution

Let Y have a Poisson distribution with the mean (Lambda). Find E[Y(Y-1)] and then use this to show that V(Y)=Lambda

Binomial Probability Distribution

Goranson and Hall explain that the probability of detecting a crack in an airplane wing is the product of p1, the probability of inspecting a plane with a wing crack; p2, the probability of inspecting the detail in which the crack is located; and p3, the probability of detecting the damage. a) what assumptions justify the multiplication of these probabilities b) p1= .9 p2 = .8 and p3 = .5 for a certain fleet of planes. If three planes are inspected from this fleet, find the probability that a wing crack will be detected in at least one of them.