A manufacturer sells two products, one at a price of $3000 a unit and the other at a price of $12000 a unit. A quantity q1 of the first product and q2 of the second product are sold at a total cost of $5000 to the manufacturer.
Express the manufacturer's profit, as a function of q1 and q2.
p = 3000 q1 + 12000 q2 - 5000
To express the manufacturer's profit as a function of q1 and q2, we need to understand that profit is calculated by subtracting the cost of producing the products from the revenue generated from selling the products.
Let's start by calculating the revenue generated from selling the first product at a price of $3000 per unit. The revenue from selling q1 units would be:
Revenue1 = q1 * $3000
Similarly, the revenue generated from selling the second product at a price of $12000 per unit would be:
Revenue2 = q2 * $12000
Now, we can calculate the total revenue generated from selling both products by summing up the revenues of each product:
Total Revenue = Revenue1 + Revenue2
The cost of selling q1 units of the first product and q2 units of the second product is given as $5000.
Profit = Total Revenue - Cost
Profit = (Revenue1 + Revenue2) - $5000
Substituting the calculated revenue values:
Profit = (q1 * $3000 + q2 * $12000) - $5000
Hence, the manufacturer's profit can be expressed as the function:
Profit(q1, q2) = (q1 * $3000 + q2 * $12000) - $5000