A company, Duzi Infrastructure, is considering whether it should propose two contracts $($Contract$-$A and Contract$-$B$)$ on offer from a government department for the supply of certain components. Duzi Infrastructure has three options:

propose for Contract$-$A only; or

propose for Contract$-$B only; or

propose for both Contract$-$A and Contract$-$B$.$

If proposals are to be submitted the company will incur additional costs. The cost of proposing for Contract$-$A only is $$30,000.$ The component supply cost if the proposal is accepted would be $$18,000.$ The cost of proposing for Contract$-$B only is $$14,000.$ The component supply cost if the proposal is accepted would be $$8,000.$ The cost of proposing for both Contract$-$A and Contract$-$B is $$43,000.$ The component supply cost if the proposal is accepted would be $$24,000.$

For each option $($Contract$-$A only; Contraction$-$B only; and Contraction$-$A and Contraction$-$B both$)$ possible prices that Duzi Infrastructure will take are determined differently depending the bidding condition; that is$,$ how competitive the bidding is$.$ The below table shows how the possible prices vary for each bidding condition and option.

$\backslash$table$[[$Options$,$Bidding condition,Probability,Price $($$$)],[$Contract$-$A only,Competitive,$0\mathrm{.}2,100,000],[$Non$-$competitive,$0\mathrm{.}8,130,000],[$Competitive$,0\mathrm{.}4,60,000],[,$Neural,$0\mathrm{.}25,90,000],[,$Non$-$competitive,$0\mathrm{.}35,15000],[\backslash$table$[[$Contract$-$A and Contract B$],[$both$]],$Competitive,$0\mathrm{.}6,190,000],[$Non$-$competitive,$0\mathrm{.}4,]]$

To maximize the profit $($Price $-$ estimated cost$),$ what options Duzi Infrastructure should take? Answer using decision$-$tree analysis.