When the quantities of the work items are difficult to be quantified and the rate analysis is also a complex issue, but still the contractor is willing to undertake a work, then the type of Contract best suited is:

Correct option is C

In a Lump Sum Contract, the contractor agrees to complete the entire project for a fixed total cost.
It is suitable when:
Quantities of work items are difficult to quantify accurately.
Rate analysis is complex.
Both parties agree on a lump sum payment, avoiding detailed measurements for payments.
Why Lump Sum Contract is Preferred in This Case:
It simplifies the payment structure as the contractor undertakes the work for a predetermined price without needing to provide detailed measurements or itemized breakdowns.
It transfers the risk of cost variations to the contractor.