Question

An orange grower has discovered a process for producing oranges that requires two inputs. The production function is Q = min{2x1, x2}, where x1 and x2 are the amounts of inputs 1 and 2 that he uses. The prices of these two inputs are w1 = $5 and w2 = $2, respectively. The minimum cost of producing 140 units is therefore

a. $980.
b. $630.
c. $1,400.
d. $280.
e. $700.

Answer 1

Answer:

Option (B) is correct.

Explanation:

The prices of two inputs 1 and 2 are as follows:

w1 = $5

w2 = $2

Q = min{2x1, x2}

Cost is minimized when 2x1 = x2

140 = min{2x1, x2}

2x1 = 140

x1 = 70

x2 = 2x1 = 140

Total cost, C = w1.x1 + w2.x2

                     = 5x1 + 2x2

C($)  = (5 × 70) + (2 × 140)

        = 350 + 280

        = $630