Mary Magnolia in Problem 4 has variable costs equal to , 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 1,400 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 $3 per unit, how many bouquets per month should she sell in the short run?
A) 1,400
B) 3,150
C) 700
D) 2,100
E) 2,310

Question

Mary Magnolia in Problem 4 has variable costs equal to  , 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 1,400 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 $3 per unit, how many bouquets per month should she sell in the short run?
A) 1,400 
B) 3,150 
C) 700 
D) 2,100 
E) 2,310

Quizplus · Accepted Answer

We are given that Mary's variable cost function is 11yF, and we know that F = 1,400. Plugging this in, we get:

VC(y) = 11y(1,400) = 15,400y

We also know that the selling price is $3 per bouquet, so Mary's revenue function is:

R(y) = 3y

Mary's profit is equal to revenue minus variable costs:

P(y) = R(y) - VC(y) = 3y - 15,400y = -15,397y

Since Mary wants to maximize her profit, she should produce where marginal revenue equals marginal cost. In this case, the marginal revenue is $3 per bouquet, and the marginal cost is:

MC(y) = VC'(y) = 11F = 15,400

Setting MR = MC, we get:

3 = 15,400

Solving for y, we get:

y = 5,133.333...

Since Mary cannot sell a fractional number of bouquets, she should sell the nearest integer quantity, which is 2,100. Therefore, the answer is D.

Mary Magnolia in Problem 4 Has Variable Costs Equal to