Question

"there are two kinds of products (called DA and GA) produced in your company every day. Also, there are two kinds of materials (denoted by A and B) in need. One DA costs one unit of A, one unit of B: One GA one unit of A, two units of B. You get 3000 dollars when you sell one DA and 5000 for one GA. The supply of the two materials every day is 12,22.

A) What is the maximum profit?
B) How many DA and GA should be produced every day to obtain this maximal profit?
Number of DA:
Number of GA:

Options:
a) 1000, 500
b) 500, 1000
c) 750, 750
d) 1000, 1000

Answer 1

To determine the maximum profit, we need to analyze the total revenue and total cost at different levels of output. By subtracting the total cost from the total revenue, we can calculate the profit for each quantity. The maximum profit occurs when 1 unit of DA and 1 unit of GA are produced, resulting in a profit of $7995. The correct option is d) 1000, 1000.

Step-by-step explanation:

To determine the maximum profit, we need to analyze the total revenue and total cost at different levels of output. From the given information, let's calculate the total cost for one unit of each product:

For DA, 1 unit of A and 1 unit of B are required, so the total cost is $1 (A) + $1 (B) = $2.
For GA, 1 unit of A and 2 units of B are required, so the total cost is $1 (A) + $2 (B) = $3.

Now, let's calculate the total revenue for each product:

For DA, the selling price is $3000, so the total revenue is $3000 * 1 = $3000.
For GA, the selling price is $5000, so the total revenue is $5000 * 1 = $5000.

Next, we need to find the maximum profit. We can calculate the profit by subtracting the total cost from the total revenue. By comparing the profits for different quantities, we can determine the maximum profit. Since the options provided are not clear, I will answer without considering the options. Let's calculate the profit for different quantities of DA and GA:

Quantity of DAQuantity of GATotal RevenueTotal CostProfit00$0$0$010$3000$2$299801$5000$3$499711$8000$5$7995

From the table, we can see that the maximum profit is $7995 when 1 unit of DA and 1 unit of GA are produced. Therefore, the correct option is d) 1000, 1000.