Context:

Joan King is marketing director for the BurgerRama restaurant chain. BurgerRama has decided to have a cartoon- character doll made to sell at a premium price at participating BurgerRama locations. The company can choose from several different versions of the doll that sell at different prices. King's problem is to decide which selling price will best suit the needs of BurgerRama's customers and store managers. King has data from previous similar promotions to help her make a decision.| Selling Price of Each Doll Number Supplied per Week per Store Number Requested per Week per Store $1.00 35 530 $2.00 130 400 $4.00 320 140 400 500 demand 300 Quantity of dolls per week per store 200 Supply 100 2 3 4 5 6(1. Estimate the price where supply and demand will be in equilibrilm1. Explain how you knew your answer. An estimated price where supply and demand will be in equilibrium is Q, 240} I knew my answer by going back to my graph and looking where the lines intersect. From the Mathematics Teacher, October 1991 4. Using equations a. Use two of the points given to nd the equation for supply (S) as a function of price (P). Make sure you write your answer in function notation with the appropriate variables. YOU MUST SHOW WORK (pg):(l,35) another point (2,130) is also on curve. (P: 53i1,35)3d(P2,53)={2:130) 335: 13035 2.1 413.1) 335=95 (p1) s=95p95+35=95p60 3 =95 6t] b. Use two of the points given to find the equation for demand (D) as a function of price (P). Make sure you write your answer in function notation with the appropriate variables. YOU MUST SHOW WORK (pl.d1)=(1, 530) (p2, d2)=(4, 140) d-140=140-530 4-1_(p-4) d-140=-390 3 (p-4) d=140-130p+520 d=-130p+660 D(P)=-130p+660 From the Mathematics Teacher, October 1991c. Algebraically solve the system of supply-and-demand equations to find the price in exact equilibrium. YOU MUST SHOW WORK d. How does your answer to 4c compare with your answer to 3d