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.
To express the manufacturer's profit as a function of q1 and q2, we first need to calculate the total revenue generated from the sales.
The revenue from selling the first product can be calculated by multiplying the price of the first product ($3000) by the quantity sold (q1), which gives us 3000q1.
Similarly, the revenue from selling the second product can be calculated by multiplying the price of the second product ($12000) by the quantity sold (q2), which gives us 12000q2.
The total revenue is the sum of these two revenue components:
Total Revenue = Revenue from the first product + Revenue from the second product
= 3000q1 + 12000q2
Next, we need to calculate the manufacturer's cost. Given that the total cost to the manufacturer is $5000, we can say:
Total Cost = $5000
Now, to find the manufacturer's profit, we subtract the total cost from the total revenue:
Profit = Total Revenue - Total Cost
= 3000q1 + 12000q2 - 5000
Therefore, the manufacturer's profit, as a function of q1 and q2, can be expressed as:
Profit(q1, q2) = 3000q1 + 12000q2 - 5000