Question

Polly’s Pasta and Pizza Supply sells wholesale goods to local restaurants. They keep track of revenue earned from selling kitchen supplies and food products. The function ​K m​ odels revenue from kitchen supplies in a given month and the function ​F ​models revenue from food product sales for a given month, where ​t represents the number of the month (January is month 1, February is month 2, etc.)

Answer 1

Complete question :

Polly’s Pasta and Pizza Supply sells wholesale goods to local restaurants. They keep track of revenue earned from selling kitchen supplies and food products. The function K models revenue from kitchen supplies and the function F models revenue from food product sales for one year in dollars, where t represents the number of the month (1 – 12) on the last day of the month.

K(t)=15t^3–312t^2+1600t+1100

F(t)=36t3–720t2+3800t–1600

In which month was her revenue from food products the greatest? The least?

Answer:

greatest revenue = 4384

Leat revenue = 400 ; October

Step-by-step explanation:

Using the model :

Claculating the revenue from. Food sales from January through December :

F(t)=36t^3–720t^2+3800t–1600

Put t = 1, 2, 3,.. 12 for January through December

t = 1

F(1)=36(1^3) - 720(1^2) + 3800(1) - 1600 = 1516

t = 2

F(2) = 36(2^3) - 720(2^2) + 3800(2) - 1600 = 3408

Inputting the t values up to 12 to cover for January thkorugh December :

We have the data:

t1 = 1516

t2 = 3408

t3 = 4292

t4 = 4384

t5 = 3900

t6 = 3056

t7 = 2068

t8 = 1152

t9 = 514

t10 = 400

t11 = 996

t12 = 2528

Hence, greatest revenue = 4384 (month of April)

Least revenue is at t10(October) ; Lowest revenue is at t 10 = 400