A certain diet requires no more than 60 units of carbohydrates, at least 45 units of protein, and at least 30 units of fat each day. Each ounce of Supplement A provides 5 units of carbs, 3 units of protein, and 4 units of fat. Each ounce of Supplement B iprovides 2 units of carbs, 2 units of protein, and 1 unit of fat. If Supplemnet A cost $1.50 per once and Supplemnt B costs $1.00 per ounce, how many ounces of each upplement should be taken daily to minimize the cost of diet?
PLEASE HELP!
i can't come up with system of
equations for this thingg..
Let C,P and F denote carbohydrates, protein and fat. Let D denote what the diet requires. Then we're told
60C<=D
D<=45P
D<=30F
A = 5C + 3P + 4F
B = 2C + 2P + 1F
A=1.50
B=1.00
We want to maximize
xA+yB=D
where x is the number of Aoz and y is Boz.
and minimize
1.50x+1.00y=cost
There are a number of ways to solve this, but considering the size of the numbers you might just make a table that starts at x=0 and y=30 and find the feasible set of values, then find which has the smallest cost in the feasible set.
After I reviewed my preious post I realized I could be a little more helpful.
If you use x and y for the number of oz of each supplement, then we want to know how many of each is the ideal amount for the diet and cost. We know they provide
1oz A = 5c + 3p + 4f
ioz B = 2c + 2p + 1f
In terms of c, p and f
5x+2y<=60 carb. requirement
3x+2y=>45 prot. requirement
4x+y=>30 fat requirement
We also know
x=>0 and y=>0 we are only interested in values in the first quadrant.
If you graph that set of lines and examine where they intersect you'll find vertices to test in the cost equation
1.50x+1.00y=Cost
I graphed those lines and there should be three vertices to test.
I hope this is more helpful.
find the solution to the system by graphing x+y=-3 and 3x-y=7
infinity
To find the solution to the system by graphing, let's start by rearranging the equations to be in slope-intercept form (y = mx + b).
For the first equation, x + y = -3, we subtract x from both sides to isolate y:
y = -x - 3
For the second equation, 3x - y = 7, we add y to both sides and rearrange:
y = 3x - 7
Now, we can graph these two equations on a coordinate plane.
First, we'll start with the equation y = -x - 3. To plot this line, find two points that satisfy the equation. For example, when x = 0, y = -3. When x = -3, y = 0. Plot these two points and draw a line through them.
Second, we'll graph the equation y = 3x - 7. Similarly, find two points that satisfy the equation. For example, when x = 0, y = -7. When x = 3, y = 2. Plot these two points and draw a line through them.
The two lines will intersect at a single point on the graph. The coordinate of this point represents the solution to the system of equations.
To find this solution, you can visually estimate the point of intersection or use additional tools like a ruler to get a more accurate reading.