Question

Homework: Homework 14 - integer optimization and optimizatio Save Score: 0 of 1 pt 7408661 4 of 6 (1 complete) HW Score: 0%, 0 of 6 pts 14.2.17 A Question Help Soapbox is a local band that plays classic and contemporary rock. The band members charge $600 for a three-hour gig. They would like to play at least 30 gigs per year but need to determine the best way to promote themselves. The most they are willing to spend on promotion is $2,500. The possible promotion options are playing free gigs, making a demo CD, hiring an agent, handing out fliers, and creating a Web site. Each free gig costs them $250 for travel and equipment but generates about three paying gigs. A high-quality studio demo CD should help the band book 20 gigs but will cost $1,000. A demo CD made on home recording equipment will cost $400 but may result in only ten bookings. A good agent will get the band 18 gigs but will charge $1,500. The band can create a Web site for $450 and would expect to generate six gigs from this exposure. They also estimate that they may book one gig for every 500 fliers they hand out, which would cost $0.08 each. They don't want to play more than seven free gigs or send out more than 2,500 fliers, and can only produce one high-quality demo CD, produce one home demo CD, hire one agent, and make one website. Develop and solve an integer optimization model to find the best promotion strategy to maximize their profit. Which combination of promotional options and quantities maximizes the profit within the constraints? Number (Type whole numbers.) Promotional Option Free gigs High-quality demo CD Homemade demo CD Agent Fliers Web site

Answer 1

Soln

Maximize Revenue = 600*n

Such that n >= 30

Promotion <= 2500

Free Gig: Expense - 250 * a gives 3a gigs

High Quality Studio – 1000*b gives 20b gigs

Low Quality Studio – 400*c gives 10c gigs

Agent – 1500d gives 18d

Website – 450e – 6e gigs

Flyiers – 0.08*f/500 --- f gigs

So, n = 3a + 20 b + 10 c + 18d + 6e + f

Expense (E) = 250a + 1000b + 400c + 1500d + 450e + 0.08/500 f

I am using Solver. We are not allowed to upload excel. Hence uploading the screenshot of the same.

We are maximizing Revenue, so our target cell would be Total Cost (Cell D17).

By changing cells, we would select Decision Variables (ie number of units for each type of Promotion).

And then we would add the constraints.

The Screenshot below shows the constraints that were used

File Home Insert Page Layout Formulas Data Review View Foxit PDF Tell me what you want to Solver Parameters AL ZA ES Set Objective: SD5171 ËShow Queries From Table Get External New Data Q uery - Lo Recent Sources Get & Transform x Clear Reapply Advanced Connections Properties Refresh All - 3 Edit Links Connections Sort Filter Text to Columns Flash Fill - Remove Duplicates Data Validation Data Tool To: Max Min O Value of: Sort & Filter D17 By Changing Variable Cells: SC$8:$C$13 А Add Inmt in o Change Subject to the Constraints: SCS10 = integer SC$10 >= 0 SCS11 = integer SCS11 >= 0 SCS12 = integer SC$12 >= 0 SCS13 = integer SCS13 >= 0 SCS8 = integer SC$8 >= 0 SCS9 = integer SC$9 >= 0 SD$14 >= 30 Delete Gigs Number Reset All 20 Decision Variables T otal Gigs Expense Per unit Total Expense 250 1000 400 1500 0.08 450 7 Promotional Option 8 Free Gigs 9 High Quality Demo CD 10 Low Quality/Homemade Demo CD 11 Agent 12 Fliers 13 Web site 14 Total Load/Save ✓ Make Unconstrained Variables Non-Negative 0.002 Select a Solving Method: Simplex LP Options o >= 30 <= 2500 Solving Method Select the GRG Nonlinear engine for Solver Problems that are smooth nonlinear. Select the LP Simplex engine for linear Solver Problems, and select the Evolutionary engine for Solver problems that are non-smooth. Maximizing Revi o We will maximize this value Help Solve Close

Solver Output

Gigs Number 20 Promotional Option Free Gigs High Quality Demo CD Low Quality/Homemade Demo CD Agent Fliers Web site Total 10 18 0.002 Decision Variables T otal Gigs Expense Per unit Total Expense 250 1000 4001 24001 1500 250 2.5 0.08 100 450 62.5 >= 30 <= 2500 0 2500 Maximizing Rev 37500 We will maximize this value

Hence, Optimal Soln

Promotional Option	Number
Free Gigs	0
High Quality Demo CD	0
Low Quality/Homemade Demo CD	6
Agent	0
Fliers	1000
Web site	0