Mary Magnolia has variable costs equal to y²/F, where y is the number of bouquets she sells per month and where F is the number of square feet of space in her shop.If Mary has signed a lease for a shop with 400 square feet, if she is not able to get out of the lease or to expand her store in the short run, and if the price of a bouquet is $5 per unit, how many bouquets per month should she sell in the short run?

A) 200
B) 1,500
C) 1,000
D) 400
E) 1,100

We need to find the quantity of bouquets that Mary Magnolia should sell in the short run, so that she can cover her variable costs, which are dependent on the number of bouquets sold per month and the square footage of her shop. We are given the formula for her variable costs as y²/F, where y is the number of bouquets sold. We can substitute the given values in the formula and simplify it as follows:

Variable costs per bouquet = y²/F = y²/400

Now, we know that the price of a bouquet is $5 per unit, which means that Mary's revenue from selling y bouquets will be $5y. In order to cover her variable costs, her revenue needs to be greater than or equal to her variable costs, i.e.,

Revenue ≥ Variable costs
5y ≥ y²/400

Simplifying this inequality, we get:

y ≥ 400

Therefore, Mary Magnolia needs to sell at least 400 bouquets per month to cover her variable costs, given the lease and shop size constraints. The choice that corresponds to this answer is (C) 1,000.