Answer to Question #198741 in Statistics and Probability for Lucy ukoh

Question

Question 3 A software Company has just won a contract worth GH¢80m, if it delivers a successful product on time, but only GH¢40m, if this is late. It faces a problem of whether to produce the work in-house or to subcontract.

To subcontract the work would cost GH¢20m but based on past experience would have only a 90% chance of being successful. In the event of the software not being successful , there would be insufficient time to re-write the whole package internally but there would still be the options of either a late-rejection of the contract (at a further cost of GH¢10m) or a late subcontracting of the work on the same terms as before. With this late start, the local subcontractor is estimated to have only a 50 / 50 chance of producing it late. In this case, the subcontractor still has to be paid GH¢50m, regardless of whether he meets the deadline or not.

i) Calculate expected values as appropriate. iii) Recommend a course of action to the company, with reasons.

Answer 1

i)

For the work in-house:

successful product:

$E(X)=80\ m$

not successful product:

$E(X)=40\ m$

For subcontract:

the software is successful:

$E(X)=20\cdot0.9=18\ m$

the software is not successful:

late-rejection of the contract:

$E(X)=10\ m$

late subcontracting of the work:

$E(X)=0.5\cdot50=25\ m$

iii)

Recommendations: the has to try work in-house, since in this case the expected values of work cost are larger.