Answer to Question #272905 in Algebra for taha

Question #272905

a women's resource center which provides housing for women and children who comes from abusive homes is undertaking a grass roots fund raising effort wihin the community



1
Expert's answer
2021-11-29T19:04:12-0500

A women’s resource center which provides housing for women and children who come from abusive home is undertaking a grass roots fund-raising effort within the community. One component of the campaign is the sale of two types of candy bars. The profit from the candy is $0.50 and $0.75 per bar, respectively, for the two types. The supplier of the candy has offered an incentive if the total numbers of candy bars sold exceeds 2000. For each bar over 2000, an additional $0.25 will be earned by the center.


(a) Determine the function P = f (x1 , x2), where P equals the total profit in dollars and xj equals the number of bars sold of type j.


(b) If 750 and 900 bars, respectively, are sold, what is the profit expected to equal?


c) If 1500 and 2250 bars, respectively, are sold, what is the profit expected to equal?


Solution

P=f(x1,x2)=XiPi+J=12PjXjP=f(x_1,x_2)=X_iP_i+\sum_{J=1}^{2} \>P_jX_j



Where Xi=X_i= Total bar sold in excess of 2000


Pi=P_i= Incentive for each bar exceeding 2000


Pj=P_j= Profit for type j


Xj=X_j= Number of bars sold for type j for Xj2000X_j \le2000



b) Total sold =1650=1650

1650<20001650<2000

\therefore No incentive



P=0+P1X1+P2X2\therefore P=0+P_1X_1+P_2X_2

=0+0.5×750+0.75×900=0+0.5×750+0.75×900

=$1050=\$1050



c). Total sold =1500+2250=1500+2250

=3750=3750


Excess of 2000=375020002000=3750-2000

=1750=1750


P=1750×0.25+1500×0.5+2250×0.75P=1750×0.25+1500×0.5+2250×0.75


=$2875=\$2875


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