Answer to Question #180001 in Algebra for Mimi

Question

The bottles of soda sold since June at the food plant can be modeled by function N(m)=10m+300 and does selling per price bottle can be modeled byC(m)=0.6m2-5m+24 where am is the number of months since June

Answer 1

The function of number of bottles sold in month of June is N(m) = 10m +300

Price of each bottle is C(m) = 0.6m²-5m+24

where, m = number of months since June

In June,

number of bottles sold N(1) = (10*1)+300 = 310

price of each bottle C(1) = 0.6(1)²-5(1)+24 = 19.6

In July,

number of bottles sold N(2) = (10*2)+300 = 320

price of each bottle C(2) = 0.6(2)²-5(2)+24 = 16.4

In August,

number of bottles sold N(3) = (10*3)+300 = 330

price of each bottle C(3) = 0.6(3)²-5(3)+24 = 14.4

In September,

number of bottles sold N(4) = (10*4)+300 = 340

price of each bottle C(4) = 0.6(4)²-5(4)+24 = 13.6

In October,

number of bottles sold N(5) = (10*5)+300 = 350

price of each bottle C(5) = 0.6(5)²-5(5)+24 = 14

In November,

number of bottles sold N(6) = (10*6)+300 = 360

price of each bottle C(6) = 0.6(6)²-5(6)+24 = 15.6

In December,

number of bottles sold N(7) = (10*7)+300 = 370

price of each bottle C(7) = 0.6(7)²-5(7)+24 = 18.4

In January,

number of bottles sold N(8) = (10*8)+300 = 380

price of each bottle C(8) = 0.6(8)²-5(8)+24 = 22.4

In February,

number of bottles sold N(9) = (10*9)+300 = 390

price of each bottle C(9) = 0.6(9)²-5(9)+24 = 27.6

In March,

number of bottles sold N(10) = (10*10)+300 = 400

price of each bottle C(10) = 0.6(10)²-5(10)+24 = 34

In April,

number of bottles sold N(11) = (10*11)+300 = 410

price of each bottle C(11) = 0.6(11)²-5(11)+24 = 41.6

In May,

number of bottles sold N(12) = (10*12)+300 = 420

price of each bottle C(12) = 0.6(12)²-5(12)+24 = 50.4

In June of next year,

number of bottles sold N(13) = (10*13)+300 = 430

price of each bottle C(13) = 0.6(13)²-5(13)+24 = 59.4

We can see that the cost of each bottle firstly decreases from June to September and then from October it get increases and the number of bottles sold in each month is increases by 10.