An engineering firm won a $$2,000,000$ contract to develop a blade spar for helicopters. The blade spar is a metal tube that runs the length of and provides strength to the helicopter blade.$$ Due to the special length and size of the blade, the firm is unable to produce a single$-$piece blade spar of the required dimensions using existing extrusion equipment and material. The engineering department has prepared two alternatives for developing the blade spar: $(1)$ sectioning or $(2)$ an improved extrusion process.$$ The firm must decide which process to use.$($Backing out of the contract at any point is not an option.$)$ The risk report has been prepared by the engineering department.$$ The information from this report is explained next.$$

The sectioning option involves joining several shorter lengths of extruded metal into a blade spar of sufficient length.$$ This work will require extensive testing and rework over $12$ months at a total cost of $$1,800,000.$ Although this process will definitely produce an adequate blade spar, it merely represents an extension of existing technology.$$

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To improve the extrusion process, on the other hand, it will be necessary to perform two steps: $(1)$ improve the material used, at a cost of $$300,000$ and $(2)$ modify the extrusion press, at a cost of $$960,000.$ The first step will require six months of work, and if this first step is successful, the second step will require another six months of work.$$ If both steps are successful, the blade spar will be available at that time, that is$,$ a year from now.$$ The engineers estimate that the probabilities of succeeding in Steps $1$ and $2$ are $0\mathrm{.}90$ and $0\mathrm{.}75,$ respectively.$$ However, if either step is unsuccessful $($which will be known only in six months for Step $1$ and in a year for Step $2),$ The firm will have no alternative but to switch to the sectioning process $$ and incur the sectioning cost on top of any costs already incurred.$$

Development of the blade spar must be completed within $18$ months to avoid holding up the rest of the contract.$$ If necessary, the sectioning work can be done on an accelerated basis in six months, but the cost of sectioning will then increase from $$1\mathrm{.}8$ million to $$2\mathrm{.}4$ million.$$ The Chief Engineer, Dr$.$ Whitmann, wants to try developing an improved extrusion process.$$ Dr$.$ Whitmann reasons that this is not only cheaper $($if successful$)$ for the current project, but its expected side benefits for future projects could be sizable.$$ Although these side benefits are difficult to gauge, Dr$.$ Whitmann$$s best guess is an additional $$2$ million.$($These side benefits are obtained only if both steps of the modified extrusion process are completed successfully.$)$

$1.$ What value of side benefits would make the firm indifferent between the two alternatives?