The complete question is:
In order to prepare for your summer bash, you go to the supermarket to buy hamburgers and chicken. Hamburgers cost $2 per pound and chicken costs $3 per pound. You have no more than $30 to spend. You expect to purchase at least 3 pounds of hamburgers.
Justify your answers
Answer:
A) System of inequalities:
B) Graph: see the picture attached
C) Three possible combinations:
Explanation:
<u>A) Write the system of inequalities to represent this situaction.</u>
<u>1. Variables:</u>
<u>2. Costs:</u>
<u>3. First constraint:</u>
<u>4. Second constraint:</u>
<u>5. Additional constraints:</u>
<u>6. System of equations:</u>
<u>B) Graph </u>
You have to graph all the constraints in a x-y coordinate system.
<u>1. To graph 2x + 3y ≤ 30 graph the line 2x + 3y = 30</u>
<u>2. To graph x ≥ 3 just draw the vertical line x = 3 and shade the region to the right of it. The points of the line are included (solid line).</u>
<u>3. The constraints x ≥ 0 and y ≥ 0 </u>mean that the region is restricted to the first quadrant (including the positive axis).
<u>4. The feasible solutions</u> are the set of points inside the common regions (intersection).
With all that information the graph is the one attached. The feasible solutions is the region defined by the triangle with vertices (3,8), (3,0), and (15,0).
<u>C) Give 3 possible combinations.</u>
You can pick any three points inside the region, as long as the coordinates are integer numbers. For instance the 3 vertices are solutions:
You could also prove that (5,4), 5 pounds of hamburgers and 4 pounds of chicken meet, the inequalities.
This is how you prove it:
And you can do the same for any pairs to verify whether they are solution or not.
