The ACME Sock Company's (ASC) production function is given by Q = 30K0.4-0.7, where K and L are ASC's annual capital and labor inputs, respectively, and Q is their annual output, measured in 1000s of pairs of socks. The prices per unit of capital and labor are pk = $2000 and p = $4000, respectively. (a) (1 pt) The Lagrangian function for the problem of minimizing ASC's cost of producing 250,000 pairs of socks is (Select ] (b) (3 pts) To minimize the cost of producing 150,000 pairs of socks, ASC should use K'= (Select] units of capital and L= [Select] units of labor, and the resulting minimum cost is C = ( Select] (c) (2 pts) ASC's marginal cost when cost is minimized is approximately [Select] , and the marginal cost is (Select ] target output increases. as the The ACME Sock Company's (ASC) production function is given by Q = 30K0.420.7, where K and L are ASC's annual capital and labor inputs, respectively, and Q is their annual output, measured in 1000s of pairs of socks. The prices per unit of capital and labor are pk = $2000 and p = $4000, respectively. (a) (1 pt) The Lagrangian function for the problem of minimizing ASC's cost of producing 250,000 pairs of socks is F(K.L.A) = 30-K^(0.4).L^(0.7)-2 4 - units of (b) (3 pts) To minimize the cost of producing 150,000 pairs of socks, ASC should use K'= Select] 6.231 units of capital and L = 2.972 7.882 4.703 um cost is C = $32,449.31 3.057 10/12 PUSTASU S margmar cost when cost is minimized is approximately [ Select] ., and the marginal cost is (Select ] as the target output increases. The ACME Sock Company's (ASC) production function is given by Q = 30K0.4-0.7, where K and L are ASC's annual capital and labor inputs, respectively, and Q is their annual output, measured in 1000s of pairs of socks. The prices per [Select] respectively. F(K,L,A) = 30.K^(0.4).L^(0.7)-2(2000K+4000L -150,000) (a) (1 pt) The L F(K,L,X) = 2000K+4000L -2(30-K^(0.4).L^(0.7)-150,000) t of producing 250,000 F(K,L,X) = 30-K^(ONA).L^(0.7)-1(2000K+4000L -150) pairs of socks F(K,L,2) = 2000K+4000L -1 (30K^(0.4).L^(0.7) 150) (b) (3 pts) To minimize the cost of producing 150,000 pairs of socks, ASC should use k = 3.057 4 units of capital and L'= 2.972 units of labor, and the resulting minimum cost is C = $32,449.31 (c) (2 pts) ASC's marginal cost when cost is minimized is approximately [Select) , and the marginal cost is [Select ] as the target output increases. The ACME Sock Company's (ASC) production function is given by Q - 30K0.4L0.7where K and L are ASC's annual capital and labor inputs, respectively, and Q is their annual output, measured in 1000s of pairs of socks. The prices per unit of capital and labor are pk = $2000 and p = $4000, respectively. (a) (1 pt) The Lagrangian function for the problem of minimizing ASC's cost of producing 250,000 pairs of socks is F(K,L,X) = 30-K^(0.4).L^(0.7)-2 4 (b) (3 pts) To minimize the cost of producing 150,000 pairs of socks. ASC should use K*- Select) 4 units of capital and L Select ] 7.109 units of 2.972 labor, and the resulting minimum cost is C = $32,449 4.115 6.385 c) (2 pts) ASC's marginal cost when cost is minimized Is approximately [Select) 9, and the marginal cost is [ Select ] as the carget output increases. The ACME Sock Company's (ASC) production function is given by Q = 30K0.420.7, where K and L are ASC's annual capital and labor inputs, respectively, and Q is their annual output, measured in 1000s of pairs of socks. The prices per unit of capital and labor are pk = $2000 and pi = $4000, respectively. (a) (1 pt) The Lagrangian function for the problem of minimizing ASC's cost of producing 250,000 pairs of socks is F(K,L,X) = 30-K^(0.4).L^(0.7)-2 4 (b) (3 pts) To minimize the cost of producing 150,000 pairs of socks, ASC should use K*= [Select] units of capital and L = [Select] 4 units of labor, and the resulting minimum cost is C = (Select ] as the (c)(2 ots) ASC's marginal cost when cost is minimized is approximately Select ] $156.75 , and the marginal cost is Select ] $177.81 $124.69 $203.22 The ACME Sock Company's (ASC) production function is given by Q = 30K0.4L0.7, where K and L are ASC's annual capital and labor inputs, respectively, and Q is their annual output, measured in 1000s of pairs of socks. The prices per unit of capital and labor are pk = $2000 and p1 = $4000, respectively. (a) (1 pt) The Lagrangian function for the problem of minimizing ASC's cost of producing 250,000 pairs of socks is F(K,L,X) = 30-K^(0.4)-L^(0.7)-2 4 (b) (3 pts) To minimize the cost of producing 150,000 pairs of socks, ASC should use K*= [Select) units of capital and L= ( Select] units of labor, and the resulting minimum cost is C= (Select] as the (c) (2 pts) ASC's marginal cost when cost is minimized is approximately [Select] Select] . and the marginal cost constant target output increases. frilly increasing decreasing The ACME Sock Company's (ASC) production function is given by Q = 30K0.4-0.7, where K and L are ASC's annual capital and labor inputs, respectively, and Q is their annual output, measured in 1000s of pairs of socks. The prices per unit of capital and labor are pk = $2000 and p1 = $4000, respectively. (a) (1 pt) The Lagrangian function for the problem of minimizing ASC's cost of producing 250,000 pairs of socks is F(K.L.A) = 30-K^(0.4).L^(0.7)-2 4 (b) (3 pts) To minimize the cost of producing 150,000 pairs of socks, ASC should use K = [Select) units of capital and L = [ Select) units of Select) labor, and the resulting minimum cost is C $28,328.77 $21,475.43 () (2 pts) ASC's marginal cost when cost is $25,863.90 (Select) .. and the m $32,449.31 as the target output increases