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Question 509198: Aman decides to eat breakfast at Burger King. He is a big fan of their French toast sticks and he likes orange juice. He wants to eat no more than 500 calories and consume no more than 450 mg of sodium. Each French toast stick (with syrup) has100 calories and 100 mg of sodium. Each small orange juice has 150calories and 50 mg of sodium. The number of French toast sticks and the number of small orange juices ordered must both be greater than or equal to zero.
a.)Define your variables, x and y.
100x+150y<500
100x+50y<450
b.)Set up a system of inequalities
I think there are four of them but not sure if I have the first set up to do the rest
c.) solve your system of inequalities graphically.
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
a). Define the variables:
Let  represent the number of French Toast Sticks.
Let  represent the number of small containers of orange juice.
b). Set up the Inequalities:
Calories Constraint: 
Sodium Constraint: 
Non-negative Constraints:  and 
c. Graph:
Step 1: Pick one of the inequalities and change it to an equation.
Step 2: Graph the equation from step 1.
Step 3: Pick a point on the coordinate plane that is NOT on the line you just graphed and substitute the coordinates into the original inequality. Hint: If the line DOES NOT pass through the origin, then the origin, (0,0), is a very good point to select for this step. If the line DOES pass through the origin, then select a point that has small integer coordinates, such as (1,1) or (1,0).
Step 4: If the result of step 3 is a TRUE statement, shade in the half-plane on the SAME side of the line graphed in step 2 that contains the point you selected in step 3. If the result of step 3 is a FALSE statement, shade in the OPPOSITE side of the line.
Step 5: Repeat steps 1 through 4 for each of the other inequalities. The area where ALL 4 shaded areas overlap is the feasible area, in other words, the ordered pair representing a valid answer to the problem is located in this feasible area.
Note that the 4 lines you graph will form a quadrilateral. The OPTIMUM solution to this problem, if a unique optimum exists, must be one of the vertices of this quadrilateral. If an optimum solution exists but is not unique, the set of optimum solutions will be the set of ordered pairs that forms one of the sides of the quadrilateral.
One more hint: The shading strategy that I gave you is where you shade in the half-plane that is the solution set of the inequality. If you do just the opposite, shading in the half-plane that is NOT the solution set, when you are done graphing all 4 inequalities the feasible area will be the completely unshaded area in the center of your graph -- much easier to see what you are working with. Just make sure you label your graph appropriately so that your instructor will know what you are doing.
I can provide a professional looking graph if you like, $5 to PayPal.
John
My calculator said it, I believe it, that settles it
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