Olivia wants to plant apple trees in two orchards Orchard A

Olivia wants to plant apple trees in two orchards. Orchard A (Oa) is larger than Orchard B (Ob) but is less level, rocky, and more difficult to irrigate, so that apple trees in Orchard A tend to produce less apples. Orchard B is small but the soil is rich, the land is level and apple production is higher per tree than in Orchard A. Olivia has 150 trees to plant; if she estimates the apple production in each orchard to reflect the following data, how many trees should she plant in each orchard?

Solution

Olivia should set the marginal product in Orchard A equal to the marginal product in Orchard B.

The marginal product can be found by dividing number of a apples by number of trees for each data set.

From the given table, it can be observed that the marginal product in Orchard A is a constant value of 75.

(750/10) =(1500/20) = (2250/30) = (3000/40) = (3750/50) = (4500/60) = (5250/ 70) = (6000/80) = (6750/ 90) = (7500/100) = 75

Therefore, Olivia should set the marginal product in Orchard B equal to 75. From the given data for Orchard B it can be observed that , this occurs when 80 trees are planted in Orchard B.

(6000/80) = 75

Accordingly, Olivia should plant 80 trees in Orchard B and

150 - 80 = 70 trees in Orchard A.