A firm manufactures a commodity at two different factories. The total cost of manufacturing depends on the quantities x and y supplied by each factory and is expressed by the joint cost function: C = f(x, y) = 2x 2 + xy + 2y 2 + 500 The company’s objective is to produce 200 units, while minimizing production costs. How many units should be supplied by each factory

Each factory should supply 100 units

x = 100 units

y = 100 units

Step-by-step explanation:

Since the total production must be 200 units, then x + y = 200.

The cost function can be rewritten as a function of 'x' as follows:

The value of 'x' for which the derivate of the cost function is zero, is the production level that minimizes cost:

In order to minimize production costs, each factory should supply 100 units

(a) the volume of the cone is 20/3 in3

hence, option a is correct.