SOLUTION: Would anyone like to please help me solve this problem? "The profits Alex makes on the cupcakes and doughnuts he sells at his bakery are shown in the table below: ....cupcakes:4...

Question 1011862: Would anyone like to please help me solve this problem? "The profits Alex makes on the cupcakes and doughnuts he sells at his bakery are shown in the table below: ....cupcakes:4... doughnuts:2. Alex can make at most 200 cupcakes per day and at most 300 doughnuts per day. He needs to earn a profit of at least $1,000 per day selling the cupcakes and doughnuts. Part A. If x represents the number of cupcakes sold per day and y represents the number of doughnuts sold per day, write the system of inequalities that describes the possible combinations of cupcakes and doughnuts Alex can sell to make the profit he needs.......Part B. Graph the system of inequalities in Part A to show all possible combinations of cupcakes and doughnuts Alex can sell to make the profit he needs." ...........I received the inequalities 4x+2y<1000 (the symbol should be at most) and x+y<500 (again, at most), and my answers came to be y is greater than or equaled to 500, and x is less than or equaled to 0...may someone please explain to me as to what i am doing wrong? I have no clue!!!
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
1) 4x + 2y > or = 1000
2) x + y < or = 500
*********************
using inequality 1
divide by 2
2x + y > or = 500
y > or = 500 - 2x
*********************
using inequality 2
y < or = 500 - x
**********************
combine the y inequalities
500 - 2x < or = y < or = 500 - x
500 - 2x < or = 500 - x
x > or = 0
************************
using inequalities 1 and 2 we have
x > or = (500 - y) / 2
x < or = 500 - y
(500 - y) / 2 < or = x < or = 500 - y
500 - y < or = 1000 - 2y
y < or = 500
******************************
x > or = 0 and y < or = 500
*****************************

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