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.

Question

Business

Jeremiah Wood

13 June, 18:14

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.

+3

Answers (1)

Know the Answer?

Edward Sullivan · Answer 1

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