Based on the provided data and the method to find the solutions:
1. First, we calculate the monthly increase in the production of LNG:
- The increase from January to February: [tex]\( 89,781 - 88,280 = 1,501 \)[/tex] tons
- The increase from February to March: [tex]\( 91,307 - 89,781 = 1,526 \)[/tex] tons
- The average monthly increase: [tex]\( \frac{1,501 + 1,526}{2} = 1,513.5 \)[/tex] tons
2. To find the production in April and May:
- April's production: [tex]\( 91,307 + 1,513.5 = 92,820.5 \)[/tex] tons
- May's production: [tex]\( 92,820.5 + 1,513.5 = 94,334 \)[/tex] tons
3. To determine the month when the production will reach approximately 104,489 tons:
- Starting from March with 91,307 tons, we increment the production by 1,513.5 tons each month until we reach or exceed 104,489 tons.
- Increasing March's production step-by-step:
- April: [tex]\( 91,307 + 1,513.5 = 92,820.5 \)[/tex] tons
- May: [tex]\( 92,820.5 + 1,513.5 = 94,334 \)[/tex] tons
- June: [tex]\( 94,334 + 1,513.5 = 95,847.5 \)[/tex] tons
- July: [tex]\( 95,847.5 + 1,513.5 = 97,361 \)[/tex] tons
- August: [tex]\( 97,361 + 1,513.5 = 98,874.5 \)[/tex] tons
- September: [tex]\( 98,874.5 + 1,513.5 = 100,388 \)[/tex] tons
- October: [tex]\( 100,388 + 1,513.5 = 101,901.5 \)[/tex] tons
- November: [tex]\( 101,901.5 + 1,513.5 = 103,415 \)[/tex] tons
- December: [tex]\( 103,415 + 1,513.5 = 104,928.5 \)[/tex] tons
- The month when the production reaches approximately 104,489 tons is December.
Filling in the blanks, we get:
- Approximately 94,334 tons of LNG will be produced in May,
- Approximately 104,489 tons will be produced in December.
