A firm’s production function is given by Q=2L1/2+3K1/2 Where Q, L, and K denote the number of units of output, labour and capital. Labour costs are $2 per unit, capital costs $1 per unit, and output sells at $8 per unit. Show that the profit function is π=16L1/2+24K1/2-2L-K And hence find the maximum profit and the values of L and K at which it is achieved.
A firm’s production function is given by Q=2L1/2+3K1/2 Where Q, L, and K denote the number of units of output, labour and capital. Labour costs are $2 per unit, capital costs $1 per unit, and output sells at $8 per unit. Show that the profit function is π=16L1/2+24K1/2-2L-K And hence find the maximum profit and the values of L and K at which it is achieved.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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- A firm’s production function is given by
Q=2L1/2+3K1/2
Where Q, L, and K denote the number of units of output, labour and capital. Labour costs are $2 per unit, capital costs $1 per unit, and output sells at $8 per unit. Show that the profit function is
π=16L1/2+24K1/2-2L-K
And hence find the maximum profit and the values of L and K at which it is achieved.
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