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
years.
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