It's a lot of words, but short questions. I got most of it, but I'm confused on a and c. Help would be greatly appreciated:
Theater Seven wants to increase its popularity. They want to determine the best number of newspaper (N), Radio (R), and Television (T) ads to produce in order to maximize profits. Constraints include production capacity limitations (time available in minutes) in each of three departments (technical support, design, workforce) as well as a constraint that requires the production of at least 1000 newspaper ads. The linear programming model of The Theater Seven’s problem is
Max z = 6 N + 10 R + 8 T
s.t.
24 N +20 R + 16 T < (or equal to) 36,000 Technical support
30 N +30 R + 24 T < (or equal to) 36,000 Design
6 N + 8 R + 4 T < (or equal to) 18,000 Workforce
1 N > (or equal to) 1,000 Newspaper ads
N, R, T > ( or equal to) 0
Refer to the enclosed Excel computer solution and answer the following:
a. Overtime rates in the Design are $12 per hour. Would you recommend
that the company consider using overtime in that department?
c. Suppose that the profit contribution of the Radio ad is increased by $1. How do you expect the solution to change?
Microsoft Excel 9.0 Answer Report
Target Cell (Max)
Cell Name Original Value Final Value
$B$10 MAX 0 8000
Adjustable Cells
Cell Name Original Value Final Value
$C$9 dec. variables N 0 1000
$D$9 dec. variables R 0 200
$E$9 dec. variables T 0 0
Constraints
Cell Name Cell Value Formula Status Slack
$C$12 Tech. Spport LHS 28000 $C$12<=$E$12 Not Binding 8000
$C$13 Design LHS 36000 $C$13<=$E$13 Binding 0
$C$14 Workforce LHS 7600 $C$14<=$E$14 Not Binding 10400
$C$15 Newspaper ads LHS 1000 $C$15>=$E$15 Binding 0
Microsoft Excel 9.0 Sensitivity Report
Adjustable Cells
Final Reduced Objective Allowable Allowable
Cell Name Value Cost Coefficient Increase Decrease
$C$9 dec. variables N 1000 0 6 4 1E+30
$D$9 dec. variables R 200 0 10 1E+30 0
$E$9 dec. variables T 0 0 8 0 1E+30
Constraints
Final Shadow Constraint Allowable Allowable
Cell Name Value Price R.H. Side Increase Decrease
$C$12 Tech. Spport LHS 28000 0 36000 1E+30 8000
$C$13 Design LHS 36000 0.333333333 36000 12000 6000
$C$14 Workforce LHS 7600 0 18000 1E+30 10400
$C$15 Newspaper ads LHS 1000 -4 1000 200 1000