Question 818754: I need help with a graph for this problem I keep hitting a brick wall please help me?
Family Foods makes jumbo cookies and regular cookies. The oven can make at most 200 cookies per day. Each jumbo cookie requires 2 ounces of flour, and each regular cookie requires 1 ounce of flour. There are 250 ounces of flour available. The income from each jumbo cookie is 11 cents and from each regular cookie is 5 cents. How many of each size cookie should be made to maximize income?
Answer by jsmallt9(3758)   (Show Source):
You can put this solution on YOUR website! Let j = the number of jumbo cookies made per day
Let r = the number of regular cookies made per day
j and r, as numbers of cookies, must not be negative. So:
 and 
Since the oven make at most 200 cookies per day:
Since each jumbo cookie requires 2 ounce of flour, then 2j would be the amount of flour needed for j cookies. And since each regular cookie requires 1 ounce of flour, then 1r (or just r) would be the amount of flour needed for r cookies. And since there only 250 ounces of flour available:
If one were to graph all four of these inequalities on the same graph (Treat the "j" as the x and the "r" as the y), the intersection of these would be a quadrilateral with a vertex at the origin, one side along the j axis (horizontal), another side along the r axis (vertical) and the rest of the quadrilateral in the first quadrant. (See the graph below.) The answer to the problem will be one of the 4 vertices of this quadrilateral.
One vertex is the origin, (0, 0). The next task is to find the other three vertices. For this find the point of intersection between the associated equations:
j + r = 200 and 2j + r = 250
j + r = 200 and j = 0
2j + r = 250 and r = 0
Since each jumbo cookies makes a profit of 11 cents and each regular cookie makes a profit of 5 cents, the objective function for profit (in cents) would be:
P = 11j + 5r
To find the answer to the problem, take the coordinates of a vertex and substitute them in for j and r in the equation above. This will give you the number of cents of profit for that combination of jumbo and regular cookies. Then repeat this for the other three vertices. This should give you 4 numbers for profit, one for each vertex. The largest (and smallest) possible profit will be one of these four. The answer will be the combination of j and r that produced the largest P. (The minimum profit, 0, would be for the (0, 0) vertex.)
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