So basically $7.50 x 40 = $300.00
Her budget is $7.50 per person. I sell a tri tip sandwich alone for $7.49 and with 2 sides for 9.99. What was the price on your tri tip sandwiches at the vending event that she saw? That should be her clue.
Here is the problem---she will find someone to do it at her price. They will cook ball tips or chuck roast or bottom round and call it tri tip. It happens every day.
The right thing to do is what you did---the only other thing would have been to tell her what you could do for $7.50---but cooking for only 40 people there is not much you can do for that price with 2 sides and a drink. How much is a Big Mac supersized meal?