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 = $10, respectively. The minimum cost of producing 160 units is therefore

 

$2,000. $2, 400. $800. $8,000. $1, 600.

Answer 1

Option (a).

Q = min{2x1, x2}

Cost is minimized when 2x1 = x2

160 = min{2x1, x2}

2x1 = 160

x1 = 80

x2 = 2x1 = 160

Total cost, C = w1.x1 + w2.x2 = 5x1 + 10x2

C ($) = 5 x 80 + 10 x 160 = 400 + 1,600 = 2,000