A1.3 Belinda’s Berries is a berry farm located just outside of town. All the locals know Belinda’s farm produces some of the best berries around. Belinda uses costly fertilizer on her land to increase its yield.

Belinda’s berry production is q = 27f 1>2, where f is the bags of fertilizer she uses and q is the pounds of berries she produces. Each pound of berries sells for

$2, and each bag of fertilizer costs $3. Belinda aims to maximize her farm’s surplus, which is equal to Surplus1f2 = 154f 1>22 - 13f2

a. What is the surplus-maximizing number of bags of fertilizer, f *, that Belinda should apply?

b. How many pounds of berries, q*, does Belinda’s Berries produce when Belinda uses f * bags of fertilizer?

c. Belinda’s total revenue equals the price multiplied by the quantity of berries, P * q. When Belinda’s Berries applies the quantity of bags of fertilizer that maximizes its surplus, f *, and sells the resulting quantity of berries, q *, how much total revenue does Belinda receive?