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

i believe it is c.y = 9x

rise over run. 9 units up over 1 unit right or 9/1

i think there was a typo. you wrote pat brings 3 quarts of ice-cream to the party. each serving of ice-cream is 1 6 quart. how many total servings of ice-cream does pat bring to the party? i think the bold is supposed to be 1/6. so 1 quart of ice cream = 6 servings. 6 * 3 = 18.