Question

Hilary sells makeup, primarily lipsticks and eye shadows. She sells the lipsticks for $10 and the eye shadows for $5. At a home show, she wants to sell at least $120 of these two products, knowing she has at most 20 items in her inventory that are either lipsticks or eye shadows.
She makes $7 on every lipstick and $3 on every eye shadow she sells. Use the information below:

Let x = lipsticks
Let y = eye shadows

Then $10x + $5y > $120
and x + y < 20.

The graph of these functions is shown to the right. It is impossible to sell a negative number of makeup items, so x and y both have to be greater than zero. Therefore, the functions are confined to the first quadrant.

Profit function:
P = $7x + $3y

How many lipsticks and eye shadows should be sold to maximize the total profit?
A.
The profit is maximized when 20 lipsticks and 0 eye shadows are sold.

B.
The profit is maximized when 12 lipsticks and 0 eye shadows are sold.

C.
The profit is maximized when 16 lipsticks and 4 eye shadows are sold.

D.
The profit is maximized when 4 lipsticks and 16 eye shadows are sold.

Answer 1

I think that the answer is actually c