light sets demanded at $c per set. For what prices should HOME-ALL sell these light sets to maximize its monthly profit on these items? II. Competitive Pricing Retailers often sell different brands of competing prod ucts. Depending on the joint demand for the products, the retailer may be able to set prices that regulate demand and, therefore, influence profit To answer this question, complete the following. 1. Recall that revenue is a product's selling price per item times the number of items sold. With this in mind, for mulate HOME-ALL's total revenue function for the two light set brands as a function of their prices. Suppose HOME-ALL, Inc., a national chain of home improvement retailers, sells two competing brands of motion sensor outdoor light sets, Dark-B-Gone 100 and Croyle & James, which the chain purchases for $8 per set and $10 per set, respectively. HOME-ALL's research depart- ment has determined the following two monthly demand equations for these light sets: 2. Form HOME-ALL's profit function for the two light set 3. Determine the price of each type of light set that will 4. Write a brief report to management that details your brands (in terms of their selling prices) maximize HOME-ALL's profit. pricing recommendations and justifies them D 120 40d +30c andC 680 + 30d -40c where D is hundreds of Dark-B-Gone 100 light sets demanded at Sd per set and C is hundreds of Croyle & James