If a firm is hiring variable resources d and f in perfectly competitive input markets, it will minimize the cost of producing any level of output by employing d and f in such amounts

See below.

Explanation:

Profit maximizing firms always employ resources where they have the marginal costs equal to marginal revenue.

So resources D and F will be employed in quantities such that their marginal costs of employing these resources are equal to the marginal revenue generated by these resources. This is also the profit maximizing quantity of inputs employed.

Hope that helps.

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