Is there anyway you can help me with a -e? I have a few answers already but I don't think they are correct. Thanks!

Consider a rm with a single-input production function given by: 1 (DOC) = 10 + (x 1000) Where x 2 0 denotes the quantity of input employed by the rm. Let w = 1 denote the per-unit cost of the input incurred by the rm. (a) Derive the rm's total cost function TC(-). (b) Derive expressions for the rm's total xed costs (TF C) and total variable costs (TVC(-)) based on your answer to part (a). (c) Derive the firm's marginal cost function MC (.) and find the value of output at which this function obtains a minimum. (d) Derive the firm's average total cost function ATC(.) and find the value of output at which this function obtains a minimum. (e) Verify that marginal cost equals average total cost at the minimum of the latter function