Your student government association decided to do a fundraiser to raise
money for a field trip. they decide to sell t-shirts and sweatshirts. the
profit for each t-shirt is $10 and the profit for each sweatshirt is $15.
they want to sell 50 items at most. compared to t-shirts, they want to sell
at least half as many sweatshirts, with a profit of at least $500.
after graphing what are the boundaries of the feasible region (i. e. the points that define
the region of solutions)? (hint: there should be four points)
are there any non-viable solutions within the feasible region
how many t-shirts and sweatshirts should they sell to maximize their profit
what is the maximum profit they can make?

Step-by-step explanation:

If x is the number of t-shirts, and y is the number of sweatshirts:

10x + 15y ≥ 500

x + y ≤ 50

y ≥ x/2

And since x and y can't be negative:

x ≥ 0

y ≥ 0

Graph:

desmos.com/calculator/mw6dsei6jm

The boundaries of the feasible region are:

(0, 50), (0, 33.3), (28.6, 14.3), and (33.3, 16.7)

Since x and y must be integers, any non-integer solutions are not viable.

The maximum profit will be when the most product is sold.  Since sweatshirts are more profitable, we want to sell as much of that as we can.  

So they should sell 0 t-shirts and 50 sweatshirts for a maximum profit of $750.

step-by-step explanation:

the original amount doesn't ''re just looking for the time it takes for 1/2 of the substance to we have

(1/2) =)     take the ln   of both sides

ln (1/2)   = )   and we can write

ln(1/2) = ) lne     and lne   = 1     so we have

ln(1/2) = -.1092t     divide both sides by -.1092

t = ln(1/2)/-.1092 = about 6.347 days = about 6.3 days (rounded)

70

step-by-step explanation: