Question

make inequality equation,solve word problem and sketch the graph.

cookie company makes oatmeal cookies.atleast 27 tons of oatmeal cookie dough is made each day.for better flavour oats are atleast twice the amounts of raisins.the cost of oats are $250 per ton and cost for raisins are $350 per ton.how much of both each(oats and raisins) should be used to minimize the cost?

 

Answer 1

Let amount of oats is x tons, and amount of raisins is y tons.

Total cost of the cookies C = 250x + 350y

For the best flavor, the amount of oats should be at least twice the amount of raisins so x >= 2y

(1) For best flavor and taking consideration maximum cost it is better take x = 2y  ⇒  y =x/2

The amount of oatmeal to be made is 27 tons  ⇒ oats + raisins  >= 27 tons

                                                                    ⇒ x + x/2 = 27

                                                                   ⇒3x/2=27

                                                                  ⇒x = 18 , y=x/2⇒y=9

The possiable quanties are from ( oats , raisins ) ⇒ ( 18 , 9) to (27 , 0).

Inequality functions are x + y >=27

                                     x >= 2y

                                    x >= 0 , y >= 0 

Comments

⇒ x + x/2 = 27
 ⇒3x/2=27

how did you get 3x?

x+x=2

 

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(x)+(x/2) =27

(x/1)+(x/2) =27

LCM of 1 and 2 is 2.

(2x+x)/2  =27

3x/2  =27