Limiting factor – BPP study text

Hello, the question is as follows:

“Lucky manufactures and sells three products, X, Y and Z, for which budgeted sales demand, unit selling prices and unit variable costs are as follows:

Budgeted sales demand for X is 550 units, Y is 500 units and Z is 400 units. The unit sales price for X is $16, Y is $18 and Z is $14. Material costs are : X = $8, Y= $6 and Z= $2 and labour costs are: X= $4, Y= $6 and Z= $9.

The organisation has existing inventory of 250 units of X and 200 units of Z, which it is quite willing to use up to meet sales demand. All three products use the same direct materials and the same type of direct labour. In the next year, the available supply of materials will be restricted to $4,800 (at cost) and the available supply of labour to $6,600 (at cost).

Required:
Determine what product mix and sales mix would maximise the organisation’s profits in the next year.”

In the solution, they determined that materials is the limiting factor and after calculating the amount of units per product to be produced, the budget was drawn and instead of multiplying the products with the contribution per unit, they were multiplied by the material cost per unit then by the contribution per limiting factor. Could you explain why it is so please?