. The online retailer, ADress, is offering two summer dresses, the Misty Breeze and the Tahitian Dream. Each Misty Breeze costs $41 to manufacture and publicize, while each Tahitian Dream costs $46. The manager of the company estimates that if each Misty Breeze is priced at x dollars and each Tahitian Dream at y dollars, then 101 − 5x + 4y Misty breeze dresses and 56 + 6x − 7y Tahitian Dream dresses will be sold on average every day. (a) (3 points) Express the total daily profit from the sale of the dresses as a function of x and y.

Respuesta :

Answer:

-5x² -7y² +10xy+30x+214y-6717

Step-by-step explanation:

The total cost of the dress is given by :

(101-5x +4y) × (56 +6x - 7y ) × 46

= 4141 - 205x - 664y +3576 +276x -322y

= 71x - 158y +6717

The total revenue can be expressed as:

(101 - 5x + 4y)× x + (56+6x-2y) ×y

=101x - 5x² +4xy +56y +6xy - 7y²

= -5x² -7y² +10xy +101x +56y

The  total daily profit from the sale of the dresses is :

= Revenue - cost

= -5x² -7y² +10xy +101x +56y - (71x - 158y +6717)

= -5x² -7y² +10xy +101x +56y -71x + 158y - 6717

= -5x² -7y² +10xy+30x+214y-6717