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 determine the total cost of selling q1 units of the first product and q2 units of the second product.
Let's start by calculating the total cost of selling q1 units of the first product. The price of each unit is $3000, so the total cost for q1 units would be 3000 * q1 = 3000q1.
Next, let's calculate the total cost of selling q2 units of the second product. The price of each unit is $12000, so the total cost for q2 units would be 12000 * q2 = 12000q2.
The manufacturer's total cost, C, would be the sum of these two costs: C = 3000q1 + 12000q2.
Now, the manufacturer's profit, P, can be calculated by subtracting the total cost from the total revenue. The revenue is equal to the total cost of selling the products which is given as $5000.
So, the manufacturer's profit, P(q1, q2), is given by P(q1, q2) = 5000 - (3000q1 + 12000q2).
Therefore, the function representing the manufacturer's profit as a function of q1 and q2 is P(q1, q2) = 5000 - (3000q1 + 12000q2).