Question

Suppose a firm produces two products in quantities x and y. Quantity x is 40 percent higher than y. The profit per unit sold is $100 for x and $300 for y. How much must be produced to get $7000 in profit

Answer 1

As given,

Quantity of x is 40% higher than y.

So, Let

Quantity of y = y

So, Quantity of x = y + 40% of y

= y + 0.4y

= 1.4y

Now,

Profit per unit of x = $100

Profit per unit of y = $300

Total Profit = $7000

So,

We know,

Total Profit = (Profit per unit of x * x) + (Profit per unit of y * y)

So, Using the above formula and the values as stated :-

$7000 = ($100 * 1.4y) + ($300 * y)

$7000 = $140y + $300y

$7000 = $440y

y = $7000/$440

y = 15.909

So,

x = 1.4*15.909

x = 22.272

Hence,

Inorder to get $7000 as profit x produced should be 22.27 (or 22 units) and y produced should be 15.909 (or 16 units).