Answer to Question #324474 in Math for Dee

Question

A factory uses ingredients A, B, C, D, E, and F to produce products I, II, III, IV, and V.

The following table shows the amounts of each ingredient in stock (in kg) as well as the

amount (in kg) necessary to produce 1 tonne (=1000 kg) of each type of product.

How many tonnes of each type of product should they make to use up all the ingredients

completely?

Hint: Suppose they need to make x1 tonnes of product I, x2 tonnes of product II, etc.

Then set up one equation for each of the ingredients A, B, C etc.

Solve this system of equations to find your answers.

Type of product−→ I II III IV V Amount in stock ↓

Ingredient ↓

A 10 0 8 20 10 507.4

B 10 14 12 16 8 749.2

C 7 5 17 0 7 505.1

D 9 38 7 3 0 848.6

E 15 14 0 8 6 491.7

F 21 0 10 20 10 659.5