The cost to produce bottled spring water is given by C(x) = 16x – 63 where x is the number of thousands of bottles. The total income (revenue) from the sale of these bottles is given by the function R(x) = – x 2 + 326x – 7463.
22. Since Profit = Revenue - Cost , the profit function would be (a) – x 2 + 210x – 2400 (b) – x 2 + 210x – 7400 (c) – x 2 + 310x – 7400 (d) –x 2 – 310xproduce
23. How many bottles sold will produce the maximum profit? (a) 125 (b) 155 (c) 175 (d) 185
24. What is the maximum profit? (a) Rs 14625 (b) Rs 16625 (c) Rs 22645 (d) Rs 14685
25. What is the profit when 245 thousand bottles are sold? (a) Rs 8525 (b) Rs 9225 (c) Rs 12645 (d) Rs 10685
Answers
Answer:
126
Step-by-step explanation:
The cost to produce bottled spring water is given by C(x) = 16x – 63 where x is the number of thousands of bottles. The total income (revenue) from the sale of these bottles is given by the function R(x) = – x 2 + 326x – 7463.
22. Since Profit = Revenue - Cost , the profit function would be (a) – x 2 + 210x – 2400 (b) – x 2 + 210x – 7400 (c) – x 2 + 310x – 7400 (d) –x 2 – 310xproduce
23. How many bottles sold will produce the maximum profit? (a) 125 (b) 155 (c) 175 (d) 185
24. What is the maximum profit? (a) Rs 14625 (b) Rs 16625 (c) Rs 22645 (d) Rs 14685
25. What is the profit when 245 thousand bottles are sold? (a) Rs 8525 (b) Rs 9225 (c) Rs 12645 (d) Rs 10685
Given :
The cost to produce bottled spring water is given by C(x) = 16x – 63 where x is the number of thousands of bottles.
The total income (revenue) from the sale of these bottles is given by the function R(x) = – x² + 326x – 7463.
To Find : Profit
Bottles sold will produce the maximum profit
maximum profit
profit when 245 thousand bottles are sold
Solution:
C(x) = 16x – 63
R(x) = – x² + 326x – 7463.
Profit = Revenue - Cost
p(x) = R(x) - C(x)
= – x² + 326x – 7463 - (16x - 63)
= – x² + 310x – 7400
option c)
Profit = – x² + 310x – 7400
P(x) = – x² + 310x – 7400
P'(x) = -2x + 310
P'(x) = 0 => -2x + 310 = 0 => x = 155
P''(x) = - 2 < 0
Hence Profit is maximum at x = 155
155 bottles sold will produce the maximum profit
option b)
maximum profit at x = 155
P(x) = – x² + 310x – 7400
= -(155)² + 310(155) - 7400
= Rs 16625
maximum profit is Rs 16625
option b)
profit when 245 thousand bottles are sold
x = 245
profit = -(245)² + 310(245) - 7400
= 8525
option (a) Rs 8525
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