A contractor makes two products P₁ and P₂. The four components required to make the products are subcontracted out and each of the components is made up from three ingredients A, B and C as follows:

The cost per unit of the ingredients A, B and C are a, b and c respectively. The contractor makes the product P₁ with 2 of component 1, 3 of component 2 and 4 of component 4, and the make-up cost is 15; product P₂ requires 1 of component 1, 1 of component 2, 1 of component 3 and 2 of component 4, and the make-up cost is 12. Find the cost to the contractor for P₁ and P₂. What is the change in costs if a increases to (a + 1)? It is found that the 5 units of A required for component 1 can be reduced to 4. What is the effect on the costs?