Provide an appropriate response.The Cobb-Douglas production function for a company is given by P(k, l) = 163k1/5l4/5 where P is the monthly production value when k is the number of units of capital and l is the number of units of labor. Suppose that capital costs $105 per unit, labor costs $70 per unit, and the total cost of capital and labor is limited to $152,250. Use Lagrange Multiplier's to write the system of equations you would use to find the number of units of capital and labor that maximize production.
What will be an ideal response?
 k-4/5l4/5 - 105? = 0 |
 k1/5l-1/5 - 70? = 0 |
| 105k + 70l - 152,250 = 0 |
Mathematics
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