Revenue Function, Profit Function and Maximum Profit

Problem: A company makes cameras. The price per camera at which x million cameras can be sold is: p(x) = 94.8 – 5x. 0 -< x -< 15 (the symbol -< is the “greater or equal to sign”, I couldn’t get it to work on my computer) The cost of making x million cameras is: c(x) = 156 + 19.7x (x is in millions of ...continues

Matrices and 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 o ...continues

Profit functions

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 ...continues

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 mul ...continues

Probability

1) A drawer contains n=5 different and distinguishable pairs of socks (a total of 10 socks). If a person randomly selects 4 socks, what is the probability that there is no matching pair in the sample? 2) A drawer contains n different and distinguishable pairs of socks (a total of 2n socks). A person randomly selects 2r o ...continues

Linear programming-maximze advertising budget

As part of a campaign to promote its annual clearance sale, the Excelsior Company decided to buy television advertising time on Station KAOS. Excelsior's advertising budget is $102,000. Morning time costs $3000/minute, afternoon time costs $1000/minute, and everning (prime) time costs $12,000 minute. Becasue of pervious commitme ...continues

Maximum profit

A farmer grows two crops, corn and soybeans. Suppose that each acre planted with corn requires 1 man day of labor, $3 investment and yields a profit of $35 at harvest. Each acre of soybeans on the other hand requires 2 man days of labor,$1 investment and returns a profit of $20 at harvest. The farmer had a total of 70 acres avai ...continues

Simplex Method

A nutritionalist is preparing a supplement mixture to add to a preparation of oatmeal. The nutritionalist has 3 mixtures available that can be combined to give the desired mixture. Each gram of the first mixture contains 1 unit of calcium, 1 unit of iron, and cost 70 cents. Each gram of the second mixture contains 1 unit of calc ...continues

It is dealing with finite automatons

(a)For each of the following languages over the unary alphabet {a}, construct a finite automaton accepting it. i. {a^2} ii. {a^2, a^3, a^4} (b) Let A be any finite nonempty subset of {a, a^2, a^3, a^4,...}. Is there always a finite automaton that accepts A?