Question

optimization problem , please write clear and follow steps please!

7) You are the business manager for a concert, and need to determine what to charge for tickets to maximize profit. By doing a linear regression (line of best fit) based on past concert data, you determined that about 3500 people would come if the tickets cost $12, and we would lose about 30 people for every dollar we raised the price. Our costs to produce the concert were $8,000.

Answer 1

charge for tickets=3 = 12+1 from past concert data, 3600 people would come if the tickets Cost $ 12. Now, (3500 – 300) x (12+ x) = Po Above relation is find by the fact 30 people lose for every dollar we raised the price P= 3500 X12 + 3500 X X – 360 21-3042 For maximize Po dlo -0. 3500 - 360 – 60 x = 0 3140 - 60x=0 x= 3140 - 314 - 52.33 60 6 Since d² Po = – 60 <0 (Maxima) daz dn Charge for ticket Required = 12 +2 = 12 +52.33 = 64.33 Profit = Po- Cost to produce Concert = 124 163:33— 8000 = 116 16 3.33