plz explain this

Question

A popular cereal combines wheat and corn.  At least 27 tons of the cereal is to be made.  For the best flavor, the amount of corn should be at least twice the amount of wheat.  Corn costs $250 per ton and wheat costs $350 per ton.  How much of each should be used to minimize the cost? 

  

 

 

Answer 1

Given

Cereal is combination of wheat and corn

The amount of cereal to be made is 27 tons

Let amount of corn is x tons

Let amount of wheat is y tons

Cost of corn per ton is $250

Cost of wheat per ton is $350

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

(1) For best flavor and taking consideration of cost of corn & wheat to minimize the  total cost it is better take x = 2y  ⇒  y =x/2

The amount of cereal to be made is 27 tons  ⇒ corn + wheat  = 27 tons

                                                                    ⇒ x + x/2 = 27

                                                                   ⇒3x/2=27

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

Amount of corn is 18 tons

Amount of wheat is 9 tons

Total cost = ( amount of corn ) ( cost of corn )  + ( amount of wheat )  ( cost of wheat )

                 =18 × 250 + 9 × 350

                 =7650

Cost of corn =18 × 250 = 4500

Cost of wheat = 9 × 350 = 3150

Total cost of cereal is = 7650