Answer to Question #272905 in Algebra for taha

Question

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

Answer 1

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

$P=f(x_1,x_2)=X_iP_i+\sum_{J=1}^{2} \>P_jX_j$

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

$P_i=$ Incentive for each bar exceeding 2000

$P_j=$ Profit for type j

$X_j=$ Number of bars sold for type j for $X_j \le2000$

b) Total sold $=1650$

$1650<2000$

$\therefore$ No incentive

$\therefore P=0+P_1X_1+P_2X_2$

$=0+0.5×750+0.75×900$

$=\$1050$

c). Total sold $=1500+2250$

$=3750$

Excess of $2000=3750-2000$

$=1750$

$P=1750×0.25+1500×0.5+2250×0.75$

$=\$2875$