Mysonic produces Prism$45,$ its flagship brand and model of large screen TV$.$ The total cost of producing

one unit of this TV brand$/$ model is $$2,160.$ Following is the channel structure of Mysonic, with margin

chain information in the network.

Question:

$(1)$ What should be the retail price of Prism$45?$

$(2)$ The manager of Mysonic expects to experience cost fluctuations in the market and has

therefore suggested a retail price of $$6,000.$ Given the above margin policies and the

suggested retail price of $$6,000,$ what would be the cost of a Prism$45$ TV to a wholesaler?

$(3)$ The suggested retail price of $$6,000$ makes sense with a producer cost of $\_\_\_\_\_\_\_\_\_\_$ with the

given margin requirements?

$(4)$If the unit total cost remains at $$2,160,$ Mysonic is considering switching to a $25\%$ mark$-$up on

cost policy in dealing with its wholesalers. How much will the wholesaler pay Mysonic for a unit

of Prism$45$ large screen TV with this switch to this $25\%$ mark$-$up policy?

$(5)$ Assume that Mysonic decides to adopt the $25\%$ mark$-$up on cost policy while the wholesalers

and retailers stick with their margin policy of $20\%$ and $40\%,$ respectively. A Prism$45$ that costs

$$2,160$ to produce will sell for $\_\_\_\_\_\_\_\_$ at retail.