A packaging firm relies on the production function Q = KL + K, with MPL = K

Question:

A packaging firm relies on the production function Q = KL + K, with MPL = K and MPK = L + 1. Assume that the firm's optimal input combination is interior (it uses positive amounts of both inputs). Derive its long-run total cost curve in terms of the input prices, w and r. Verify that if the input prices double, then total cost doubles as well.