Peter and John operates on a technology described by the following production function: Q = L2 + 5LK + K2 where Q = Quantity of output. L = Quantity of labour. K = Quantity of capital. (a) Determine its isoquant for Q = 100. (b) Derive the MPP’ function if K = 10. (c) If K=10 where do diminishing returns to labour set in? (d) If the price of labour equals Rs. 5 and that of capital equals Rs. 10 and the company wishes to produce 45,000 units of its production, determine the least-cost-input combination that the company must employ.

Peter and John operates on a technology described by the following production
function:
Q = L2
+ 5LK + K2
where Q = Quantity of output.

L = Quantity of labour.
K = Quantity of capital.
(a) Determine its isoquant for Q = 100.
(b) Derive the MPP’ function if K = 10.
(c) If K=10 where do diminishing returns to labour set in?
(d) If the price of labour equals Rs. 5 and that of capital equals Rs. 10 and the
company wishes to produce 45,000 units of its production, determine the
least-cost-input combination that the company must employ.