need to figure out how much i can afford to spend per person,per week for food to supply elderly food program

Question

I receive $32 per week per person from government donation, a total of 33600 elderly and my fixed cost is $36,000. please help. I need to know how much i can afford to spend per person, per week for food to supply the program and still beak-even. food expense is my only variable expense.

Answer 1

If food is variable, let's call it f. You have $32/week/person as income, and for expenses you have $36,000 in fixed expenses (I'm assuming that's per week) and 33,600f in food expenses (33,600 people * the cost of food per person). So your inequality is then:

32*33,600 - (36,000 + 33,600f) >= 0

This says that your income minus your expenses has to be equal to or greater than 0. Solving, you have:

1,075,200 - 36,000 - 33,600f >= 0
1,039,200 >= 33,600f
30.93 >= f

So this says that if you spend $30.93 per person per week, you'll break even. Anything less than that gives you a profit.