Final answer:
In the short run, Mary Magnolia should sell enough bouquets to cover her variable costs and some of her fixed costs. Her variable costs are calculated based on the number of bouquets she sells per month and the square footage of her shop.
Step-by-step explanation:
In the short run, Mary Magnolia should sell enough bouquets to cover her variable costs and some of her fixed costs. Her variable costs are calculated as y2/f, where y is the number of bouquets she sells per month and f is the number of square feet of space in her shop. Since Mary has signed a lease for a shop with 800 square feet and cannot get out of the lease, she needs to generate enough revenue to cover the fixed cost of the lease as well.
To determine how many bouquets Mary needs to sell to cover her fixed and variable costs, let's assume that the price of a bouquet is $6 per unit. We can set up the equation:
Total Revenue = Price * Quantity = $6 * y = $6y
Total Cost = Fixed Cost + Variable Cost = f + y2/f
For Mary to break even in the short run, her Total Revenue should be equal to her Total Cost. So we can set up the equation:
$6y = f + y2/f
To find how many bouquets Mary needs to sell, we can rearrange the equation:
$6y - y2/f = f
We know the value of f is 800 (the square footage of her shop) and the price per bouquet is $6. By substituting those values into the equation, we can solve for y.