Milligan, who hasn't lost any of the nine previous tasks set by Lord Sugar, objects to Hossaini's leadership skills, claiming that her rival is "floundering".
Sugar takes the remaining candidates to Enfield this week and reveals that the task will involve selling £250 worth of wholesale goods and attempting to maximise the profit with reinvestment on what they consider the most profitable items.
Hossaini is quick to take control of the task, telling the cameras: "Lord Sugar seems to be passionate about this task, it seems to be close to his heart. So I wanted to put myself forward. Although I don't have direct expertise, it's about good management. I think I'm able to deliver on that."
However, she completely ignores the advice of her team member Tom Pellereau after he strikes success with sales of a nodding dog toy early on.
"I absolutely worked my socks off today working on that stand and I'm really pissed off that the money I created has been spent unwisely by Melody," moans Pellereau.
Milligan has similar fears, adding: "I feel like Melody isn't really taking charge at all. She doesn't seem to be organised or even seem to grasp the concept of what we're meant to be doing.
"I wish I had put myself forward as project manager. I want to keep a clean sheet and I think I at least would have had a strategy and been organised and got on with things, whereas at the moment we're just floundering."
When Milligan approaches Hossaini about taking over as PM, her rival declines the offer, defiantly proclaiming: "I'm project manager and I actually want to lead on this. I want to take responsibility because that's what I've put myself forward to do and that's it."
The Apprentice airs tonight at 9pm on BBC One.
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