A store sells two brands of camping chairs. The store pays $30 for each brand A chair and $10 for each brand B chair. The research department has estimated that the weekly demand equations for these two competitive products to be the following, where p is the selling price for brand selling price for brand B, and x and y are the average number of chairs sold per week. Complete parts (A) and (B) below. x = 533-3p+q y = 358+p-2q Demand equation Demand equation r brand A brand B (A) Determine the demands for x and y when p=$70 and q=$130. The demand for x will be (Type a whole number.) The demand for x will be (Type a whole number.) The demand for y will be (Type a whole number.) Determine the demands for x and y when p= $120 and q= $90. The demand for y will be (Type a whole number.) (B) How should the store price each chair to maximize weekly profits? What is the maximum weekly profit? [Hint: C=30x+10y, R=px+qy, and P=R-C] The equation for P is P(p,q) =- To maximize profit, the brand A chair should be priced at $ and the brand B chair should be priced at $ (Type integers or decimals rounded to two decimal places as needed.) The maximum weekly profit is $ per week. (Type an integer or decimal rounded to two decimal places as needed.)

Algebra for College Students

10th Edition

ISBN:9781285195780

Author:Jerome E. Kaufmann, Karen L. Schwitters

Publisher:Jerome E. Kaufmann, Karen L. Schwitters

Chapter12: Algebra Of Matrices

Section12.CR: Review Problem Set

Problem 37CR

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Transcribed Image Text:A store sells two brands of camping chairs. The store pays $30 for each brand A chair and $10 for each brand B chair. The research department has estimated that the weekly demand equations for these two competitive products to be the following, where p is the selling price for brand A, q is the selling price for brand B, and x and y are the average number of chairs sold per week. Complete parts (A) and (B) below. x = 533-3p + q y = 358 +p-2q Demand equation for brand A Demand equation for brand B (A) Determine the demands for x and y when p = $70 and q = $130. The demand for x will be (Type a whole number.) The demand for y will be (Type a whole number.) Determine the demands for x and y when p = $120 and q = $90. The demand for x will be (Type a whole number.) The demand for y will be (Type a whole number.) (B) How should the store price each chair to maximize weekly profits? What is the maximum weekly profit? [Hint: C=30x+10y, R= px + qy, and P=R-C.] The equation for P is P(p,q) = To maximize profit, the brand A chair should be priced at $ and the brand B chair should be priced at $ (Type integers or decimals rounded to two decimal places as needed.) C The maximum weekly profit is $ per week. (Type an integer or decimal rounded to two decimal places as needed.)

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