Maximizing profit. A store sells two brands of laptop sleeves. The store pays $25 for each brand A sleeve and $30 for each brand B sleeve. A consulting firm has estimated the daily demand equations for these two competitive products to be x = 130 − 4 p + q Demand equation for brand A y = 115 + 2 p − 3 q Demand equation for brand B where p is the selling price for brand A and q is the selling price for brand B . (A) Determine the demands x and y when p = $40 and q = $50; when p = $45 and q = $55. (B) How should the store price each brand of sleeve to maximize daily profits? What is the maximum daily profit? [ Hint: C = 25 x + 30 y , R = px + qy , and P = R − C .]
Maximizing profit. A store sells two brands of laptop sleeves. The store pays $25 for each brand A sleeve and $30 for each brand B sleeve. A consulting firm has estimated the daily demand equations for these two competitive products to be x = 130 − 4 p + q Demand equation for brand A y = 115 + 2 p − 3 q Demand equation for brand B where p is the selling price for brand A and q is the selling price for brand B . (A) Determine the demands x and y when p = $40 and q = $50; when p = $45 and q = $55. (B) How should the store price each brand of sleeve to maximize daily profits? What is the maximum daily profit? [ Hint: C = 25 x + 30 y , R = px + qy , and P = R − C .]
Solution Summary: The author calculates the daily demand equations for brand A and B laptop sleeves when the selling price is 40 and 50.
Maximizing profit. A store sells two brands of laptop sleeves. The store pays $25 for each brand A sleeve and $30 for each brand B sleeve. A consulting firm has estimated the daily demand equations for these two competitive products to be
x
=
130
−
4
p
+
q
Demand equation for brand
A
y
=
115
+
2
p
−
3
q
Demand equation for brand
B
where p is the selling price for brand A and q is the selling price for brand B.
(A) Determine the demands x and y when p = $40 and q = $50; when p = $45 and q = $55.
(B) How should the store price each brand of sleeve to maximize daily profits? What is the maximum daily profit? [Hint: C = 25x + 30y, R = px + qy, and P = R − C.]
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