Ask for junior high school thinking questions and explanations, junior high school thinking exercise

A food company invested 9.22 million yuan to purchase new equipment to produce new products, in addition, the cost of producing new products is 32 yuan per piece. According to the regulations: the price of the product shall not be less than 80 yuan and shall not be higher than 120 yuan.

It is known that the functional relationship between the annual sales volume of the product y (10,000 pieces) and the product price x is y=-the square of one-eighth x + 25

1.Is the company profitable or losing money in the first year? Find the selling price of the product when the profit is the largest or the loss is the smallest.

2.Under the premise of (2), that is, the largest profit or the smallest loss in the first year, the company re-determines the product price in the second year, whether the total profit in two years can reach 8.34 million yuan, if it can find the product price in the second year, if not, explain the reasons.

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1.Let the profit be s

then s = (x-32) y-922 = (x-32) (25-x 8) -922 = (1 8) (-x 2 + 232x-6400) - 922

1/8)(x-116)^2-40

Known 80 x 120

It can be seen that the loss in the first year, the minimum loss is -400,000 yuan, and the price of the product at this time is x = 116 yuan.

2.Profit in the second year s' = (x-32)*y=882-(1 8)(x-116) 2

It can be seen that the maximum profit is 8.82 million yuan, minus the loss in the first year, there is 842>834

Therefore, it can achieve the required profit in two years.

At this time'=834+40=874

i.e. 882-(1 8)(x-116) 2=874

1/8)(x-116)^2=8

The solution is x=116-8=108 yuan.

That is, the price of the product in the second year is 108 yuan.

If you want to find the area of the shadow part, use the "cut-and-fill method".

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Set the annual planned output to be x tons, get:

31/60x+

x=2424*5%= 10,000 tons more than planned.

2.Let A deposit x and B deposit 6900-x, get:

1-1/6)x=6900-x+800

x=4200

6900-4200=2700 A originally deposited 4200, B deposited 2700

Solution: Set 45 x yuan days, and 60 seats from the question to (x+100) days.

2(x+100)+5x=1600

7x+200=1600

7x=1400

x=200 then the rock celery code.

x+100)=200+100=300

45 seats: 200 yuan per day; 60 seats: 300 yuan per day.

Solution: Set up 45 seats to rent x cars, from the question to rent 60 seats (x-2) cars.

45x+15=(x-2)*60

The front is the total number of people, 15 is drawn for 45-30.

45x+15=60x-120

135=15x

x = 7 that is, the plan of a rough is to rent 7 cars and 45 seats, ** is 7 * 200 = 1400 yuan.

B's first plan is to rent 5 cars with 60 seats, ** is 5 * 300 = 1500 yuan.

A selection plan.