Question 1186038: Solving real life problems involving functions
Meet bestfriend Jessa and chan. They have formed a partnership. Jessa being the creative one makes fashionable face masks. Chan, being business-minded, markets the face masks Jessa makes. In a recent month, they spent 600 pesos on a raw materials to make 32 pieces of masks and sold each for 30 pesos each. Assuming that they are not required to pay a sales taxes, their net profit depends on the number of pieces sold.
A. What are the three constants or fixed values in the problem?
Let use n to represent the number of pieces of face masks sold and P for the net profit
B. What should be the greatest value of n?
C. What should be the greatest value of P?
D. What should be the least value of n?
E. What should be the least value of P?
F. By a table values, show what happens to the value of as n increases.(Show 3 values of n only in the table).
G. How many pieces need to be sold so that sales and expenses are even or the same?
H. Represent as function the relation between P(n) and n.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! n = the number of masks sold.
P = the net profit = the revenue minus the cost.
C = the cost for 32 masks = 600.
the revenue is equal to 30 * n
A. What are the three constants or fixed values in the problem?
the 3 constants would be.
cost of 600 pesos for the raw materials.
sale price of 30 pesos for each face mask.
maximum number of masks that can be sold is 32.
B. What should be the greatest value of n?
the greatest value of n would be 32.
C. What should be the greatest value of P?
the maximum profit is when all masks are sold.
that would be 32 * 30 = 960 minus 600 = 360.
D. What should be the least value of n?
the least value of n would be equal to 0.
this assumes that none of the masks were sold.
E. What should be the least value of P?
P = revenue minus cost.
the cost is 600.
the revenue is 30 * the number of masks sold.
if they didn't sell any masks, then the formula becomes:
P = 0 * 30 - 600 = -600.
a profit of minus 600 means a loss of 600.
the least value of P would be -600.
F. By a table values, show what happens to the value of as n increases.(Show 3 values of n only in the table).
when n = 10, P = 10 * 30 minus 600 = 300 minus 600 = minus 300.
when n = 20, P = 20 * 30 minus 600 = 600 minus 600 = 0.
when n = 30, P = 30 * 30 minus 600 = 900 minus 600 = 300.
G. How many pieces need to be sold so that sales and expenses are even or the same?
break even point is when the profit is equal to 0.
P = 30 * n - 600
set P = 0 to get:
0 = 30 * n - 600
add 600 to both sides of this equation to get:
600 = 30 * n
solve for n to get:
n = 600 / 30 = 20.
break even point is when 20 masks are sold.
when 20 masks are sold, P = 20 * 30 - 600 = 600 - 600 = 0.
H. Represent as function the relation between P(n) and n.
P(n) = 30 * n - 600.
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