32. Answer: 2+5×3=17
33. Answer: 2×5+3=17
34. Answer: 2×5×3=30
35. Answer: 2×5-3=7
Answer:
6 titles and 16 acts were elaborated
Step-by-step explanation:
Let the number of titles be t and the number of acts be a
Since the total is 22 operations:
a + t = 22 •••••••(i)
Total amount from titles = 3500 * t = 3500t
Total amount from acts = 2000 * a = 2000a
2000a + 3500t = 53,000 ••••••(ii)
From i, a = 22-t
Insert this in ii
2000(22-t) + 3500t = 53,000
44,000 - 2000t + 3500t = 53,000
1,500t = 53000-44000
1500t = 9000
t = 9000/1500
t = 6
But a = 22 -
= 22-6 = 16
Given that 
, we have 
, so that
Take the derivative and find the critical points of 
:
Take the second derivative and evaluate it at the critical point:
Since 
is positive for all 
, the critical point is a minimum.
At the critical point, we get the minimum value 
.
