A biologist must make a nutrient of her algae...

A biologist must make a nutrient of her algae. The nutrient must contain three basic elements D, E, F, and must contain at least 10kg of D, 12kg of E, and 20Kg of F. The nutrient is made from three ingredients, I, II, III. The quantity of D, E, F in one unit of each of the ingredients is given in the following chart. Ingredient I II III Kilograms of Elements(per unit of ingredient) D 4 1 10 E 3 2 1 ... click for more

Using Simplex method minimize C...

In this problem I am trying to get rid of the artificial variable using the two phase method. However all of the rows either have negatives or zeros and my final answer keeps coming out to be a negative and none of the other answers plug into the constraints. The problem is Using Simplex method minimize C: C=15x1+12x2 Subject to 3x1+x2>18 x1+2x2<12 x1+x2=10 The numbers behind the x's are the sub numbers(x sub 1, x sub2, etc...) The greater than and less than signs are also equal to(the 1st constraint is greater than or equal to) My final answer for c = 144 Please help

Use the method incorporating the duality

A brewery manufactures 3 types of beer ---lite, regular and dark. Each vat of lite beer requires 6 bags of barley, 1 bag of sugar, and 1 bag of hops. Each vat of regular beer requires 4 bags of barley, 3 bags of sugar, and 1 bag of hops. Each vat of dark beer requires 2 bags of barley, 2 bags of sugar, and 4 bags of hops. Each day the brewery has 800 bags of barley, 600 bags of sugar, and 300 bags of hops available. The brewery realizes a profit of $10 per vat of lite beer, $20 per vat of regular beer, and $30 per vat of dark beer. How many vats of lite, regular and dark beer should be brewed in order to maximize profits? What is the maximum profit?

Probability problem

A large sports conference moved to have women compose at least 40% of its athletics within 5 years. Suppose they exactly achieve the 40% figure, and that 5 athletics are picked at random from 10 universities. The number of women is recorded. (a) give a probability distribution (b) find the expected value

Probability

Six people will decide which of them are on a committee by flipping a coin. Each person flips the coin, and is on the committee if he or she gets a head. What is the probability that someone is on the committee, but not all six people.