To win a project contract through competitive bidding, contractors submit a bid price that is determined by putting a markup on the estimated project cost. The success of the bid is therefore heavily dependent on the accuracy of that estimate, meaning that sufficient resources should be allocated to the estimation process. This paper develops a novel optimization model for simultaneously determining the bid markup and the resources that should be allocated to cost estimation. We begin by deriving optimality conditions for this simultaneous optimization model and illustrating them with numerical examples, for which purpose only we assume a single competitor and uniformly distributed estimation errors. To analyze a more realistic situation, we then examine computational solutions to our model. Through these two approaches, we investigate the effects of the bidmarkup decision and resource allocation on the contractor’s expected profit, and we highlight the significance in competitive bidding of the markup and allocation.