If y varies directly as x, and y = 25 as x = 5, find y for the x-value 7.

The production planner for Fine Coffees, Inc. Produces two coffee blends: American (A) and British (B). He can only get 300 poun

VladimirAG [237]

Answer:

P=2A+B where:

A= # of pounds of American blend and

B= # of pounds of British blend

Step-by-step explanation:

This is a linear programming problem. In order to solve it we need to determine how we are going to use the provided data and we need to keep in mind what we need to maximize (or minimize depending on the problem)

So, the problem states that "The goal of Fine Coffees, Inc. Is to maximize profits." This last sentence will tell us what the objective function will be. The objective function must model the desired value we want to maximize. So the objective function should represent the profits of selling the two tipes of cofee blends.

So this is the data the problem gives us:

"He can only get 300 pounts of Colombian beans per week and 200 pounts of Dominican beans per week." This part or the problem is talking about the amount of coffee beans he can get depending on its type. This will help us find the restrictions for our linear programming problem, so they are not necessary to state the objective function. Next it states:

"Each pount of American blend cofee requires 12 oz of Colombian beans and 4 oz. of Dominican beans, while a pound of British blend coffee uses 8 oz of each type of bean." Again, this data will help us find the restrictions for our linear programming problem, since they will tell us how much coffe we can manufacture, so they are not needed to find the objective function.

The next part states: "Profits for the American blend are $2.00 per pound, and profits for the British blend are $1.00 per pound." Now, we are interested in this part since it's talking about profits, which is what we need to maximize.

We set A to be the number of pounds of American blend and B to be the number of pounds of British blend. So the profit for American blend is found by using the following equation:

$P_{American}=$2.00*A$

And the profit for the British blend is found by using the following equation:

$P_{British}=$1.00*B$

so the total profit is found by adding the two given profits, so we get:

$P_{total}=P_{American}+P_{British}$

or

$P_{total}=$2.00A+$1.00B$

which can be simplified to:

P=2A+B

which is our objective function.

6 0

3 years ago

Which matrix represents the system of equations shown below? 3x-5y=12 4x-2y=15

tatuchka [14]

Answer:

$\left[\begin{array}{ccc}3&-5 &|12\\4&-2 &|15\\\end{array}\right]$

Step-by-step explanation:

When making a matrix of two equations with the variables x and y, the result will be a matrix with three columns:

a column for the values of x in each equation
a column for the values of y in each equation
a column for the independent values of each equation

since our system of equations is:

$3x-5y=12\\ 4x-2y=15$

we can see that the value for x in the first equation is 3 and in the second equation is 4, thus the first column will have the numbers 3 and 4:

$\left[\begin{array}{ccc}3&&\\4&&\\\end{array}\right]$

Now for the values of y we hvae -5 in the first equation and -2 in the second equation, we update the matrix with another column with the values of -5 and -2:

$\left[\begin{array}{ccc}3&-5&\\4&-2&\\\end{array}\right]$

Finally, the last column is the independent values of each equation (or the results) in the first equation that number is 12 and in the second equation is 15, thus the matrix is:

$\left[\begin{array}{ccc}3&-5&12\\4&-2&15\\\end{array}\right]$

usually there is a line separating the columns for the values of x and y, and the independent values:

$\left[\begin{array}{ccc}3&-5 &|12\\4&-2 &|15\\\end{array}\right]$

this is the matrix of the system of equations

6 0

3 years ago

Helen is 8 years older than Jane. Twenty years ago Helen was three times as old as Jane. How old is each now?

Ganezh [65]

Helen is 16 and Jane is 8

3 0

3 years ago

Read 2 more answers

The sale tax rate is 7.5%. What is the tax on a $14.80 purchase.

SSSSS [86.1K]

Okay! Assuming this only wants the tax that will be added to the total, multiply the decimal percent by the cost of the item.

7.5% = .075

14.80 * .075 = 1.11

1.11 of tax will be added onto the total cost.

The total cost would be 15.91, which you can get from adding 14.80 to 1.11 or by doing 14.80 * 1.075. Regardless, the answer to this question is 1.11.

4 0

3 years ago

Which is larger, 1.13 or 1.1301

marissa [1.9K]

1.1301 is larger cuz 1.13 is same as 1.1300

5 0

3 years ago