Demand for New Sandwiches The marketing manager of Arby\'s restaurants determine

Question

Demand for New Sandwiches The marketing manager of Arby's restaurants determines that the demand, d, for a new chicken sandwich is a linear function of the price, p, for $0.80 lessthanorequalto p lessthanorequalto $4.00. If the price is $1.00, then 530 chicken sandwiches will be sold each month. If the price is $2.00, only 400 chicken sandwiches will be sold each month. Using ordered pairs of the form (p, d), write an equation for the demand, d, as a function of price, p. Using the function from part determine the demand when the price of the chicken sandwich is $2.60. Using the function from part determine the price charged if the demand for chicken sandwiches is 244 chicken sandwiches.

Explanation / Answer

(a). Let the linear relationship between the price 'p' and the demand'd' be d = ap+b where a and b are arbitrary real numbers. Here a = (530-400)/(1-2) = -130 so that the required linear relationship chages to d = -130p +b. Now, since d = 530 when p = 1, on substituting ( d,p) = (530,1) in the equation, we get 530 = -130 +b or, b = 530 +130 = 660. Then, the required (p,d) linear relationship is d = -130p+660.

(b) When p = $ 2.6, we have d =( -130)*2.60+660 =-338+660 = 322. Thus the demand for the chicken sandwich when its price is $ 2.60 is 322.

(c ) If the demand for the chicken sandwich is 244, then, we have 244 = -130p + 660 or, 130 p = 660 -244 = 416 so that p = 416/130 =$3.20. Thus the price of the chicken sandwich, when its demand is 244, is $ 3.20.

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