the three product lines of group of company earn the following contribution margin per unit:

X - 10

Y - 15

Z - 12

All the three products require the use of materials A. The needed quantities of material A per unit of the products are 5, 3, 4 for product x, y, z. A labor strike in the company manufacturing material A limited the supply of the materials only to 200,000 units per month which is not enough to meet the monthly production requirement based on the sales demand of 20,000 for x, 10,000 for y, and 30,000 for z. Fixed manufacturing cost for the 3 products amounts to 100,000 per month.

Determine the number of units that must be produced for each product that will maximize total contribution margin and optimize utilization of the 200,000 units of material A.