A seller makes an offer of selling certain articles that can be descri...
Given information:
- x = 25 - 2y (price per unit)
- Cost price = Rs. 10 per unit
To avoid loss, the selling price should be greater than or equal to the cost price.
So, we can write the inequality:
x ≥ 10
Substituting the value of x from the given equation, we get:
25 - 2y ≥ 10
Solving for y, we get:
y ≤ 7.5
Since y represents the number of units, it cannot be a fractional value. So, we take the maximum integer value of y that satisfies the inequality:
y ≤ 7
Substituting this value of y in the given equation, we get:
x = 25 - 2(7) = 11
So, the maximum price per unit that can be offered without loss is Rs. 11.
To find the maximum quantity that can be offered in a single deal, we need to check the total revenue and total cost for different values of y.
For y = 1, x = 23
Total revenue = xy = 23(1) = 23
Total cost = 10(1) = 10
Profit = 23 - 10 = 13
For y = 2, x = 21
Total revenue = xy = 21(2) = 42
Total cost = 10(2) = 20
Profit = 42 - 20 = 22
For y = 3, x = 19
Total revenue = xy = 19(3) = 57
Total cost = 10(3) = 30
Profit = 57 - 30 = 27
For y = 4, x = 17
Total revenue = xy = 17(4) = 68
Total cost = 10(4) = 40
Profit = 68 - 40 = 28
For y = 5, x = 15
Total revenue = xy = 15(5) = 75
Total cost = 10(5) = 50
Profit = 75 - 50 = 25
For y = 6, x = 13
Total revenue = xy = 13(6) = 78
Total cost = 10(6) = 60
Profit = 78 - 60 = 18
For y = 7, x = 11
Total revenue = xy = 11(7) = 77
Total cost = 10(7) = 70
Profit = 77 - 70 = 7
For y = 8, x = 9
Total revenue = xy = 9(8) = 72
Total cost = 10(8) = 80
Profit = 72 - 80 = -8
We can see that the profit becomes negative for y = 8. So, the maximum quantity that can be offered in a single deal to avoid loss is 7 units (option b).
A seller makes an offer of selling certain articles that can be descri...
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