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Maximum profit from given cost and price functions

This type of question, asked 2 times: 20 Apr 2025 S2, 26 Apr 2025 S1. All 2 questions below, oldest first.

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  1. Question 1

    20 Apr 2025 S2

    113
    A manufacturer produces xx items per week at a total cost of ₹ ( x2+78x+2500x^{2}+ 78x+ 2500 ). The price per unit is given by 8x=600−p8x= 600 - p where ' p ' is the price of each unit. Then the maximum profit obtained is

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  2. Question 2

    26 Apr 2025 S1

    133
    A manufacturer sells xx items at a price of rupees (6−x40)\left( 6 -\frac{x}{40} \right) each. The cost price of xx items is ₹ (x5+193)\left( \frac{x}{5}+ 193 \right). The maximum profit in ₹ ____\_\_\_\_ is

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