7 The following questions refer to the Giapetto problem

(Section 3.1). Giapetto’s LP was

a Show that as long as soldiers (x1) contribute between $2 and $4 to profit, the current basis remains optimal. If soldiers contribute $3.50 to profit, find the new optimal solution to the Giapetto problem.
b Show that as long as trains (x2) contribute between $1.50 and $3.00 to profit, the current basis remains optimal.
c Show that if between 80 and 120 finishing hours are available, the current basis remains optimal. Find the new optimal solution to the Giapetto problem if 90 finishing hours are available.
d Show that as long as the demand for soldiers is at least 20, the current basis remains optimal.
e Giapetto is considering manufacturing toy boats. A toy boat uses 2 carpentry hours and 1 finishing hour. Demand for toy boats is unlimited. If a toy boat contributes $3.50 to profit, should Giapetto manufacture any toy boats?

Transcribed Image Text:

max z= 3x1 + 2x2 s.t. 2x1 + x2 100 (Finishing constraint) x1 + x2 80 (Carpentry constraint) x1 40 (Limited demand for soldiers) (x = soldiers and x2 = trains). After adding slack variables $1, $2, and $3, the optimal tableau is as shown in Table 12. Use this optimal tableau to answer the following questions: