f Sugareo is considering making Type 4 andy bars. A Type 4 cundy har earns 17% profit and requires 3 oz of sugar and 4oz of chocolate. Should Sugarco manufacture any 'Type 4 candy bars? 7 The following questions tefer to the Giapelto problen (Section 3.1). Giapetto's LP was max:3x1+2x2s.t.2x1+x2100(Fintshingconstraint)x1x280(Carpentryconstraint)x140(Limiteddemandforsoldiers) (x1= soldicrs and x2=1 rains). After adding slack variables s1,s2, and s3, the optimal tableau is as shown in Table 12 . Use this optimal tableau to answer the following questions: 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 ivailable, 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? Group B 8 Consider the Dorian Auto problem (Example 2 of Chapter 3): x1,x10 (x1= number of comedy ads, and x2= number of football ads). 'The optimal tableat is given in 'lable 13. Remember that for a min problem, a tableau is optimal if and only if cach variable has a rompositive coefficient in row 0 and the right-hand side of each constraint. is nonnegative. a Find the range of values of the cost of a comedy ad (currently $50,000 ) for which the current basis remains optimal. b Find the range of values of the number of required HIW exposures (currently 28 million) for which the eurrent basis remains optimal. If 40 million HIW exposures were required, what would be the new optinal solution? c Suppose an ad on a news program costs $110,000 and reaches 12 million HIW and 7 million HIM. Should Dorian advertise on the news program? 9 Show that if the right-hand side of the i th constraint is increased by , then the right-hand side of the optimal tableau is given by (original right-hand side of the optimal tableau) + (column i of B1). TAR I F 19 6.4 Sensitivity Analysis When More Than One Parameter Is Changed: The 100\% Rule In this setion, we show how to use the LINDO output to determine whether the current basis remains optimal when more than one objective function coefficient or right-hand side is changed. The 100% Rule for Changing Objective Function Coefficients Depending on whether the objective function coefficient of any variable with a zero reduced cost in the optimal tableau is changed, there are two cases to consider: This section covers topics that may be omitted with no loss of continuity. 6. 4 Sensitivily Analysis When More Than One Parameter is Changed: The 100\% Rule 289