Beta Ltd makes two products, X and Y. Unfortunately, although the market demand for both products is very high, the firm is unable to fully satisfy this demand for both products due to constraints in the availability of both machine capacity and skilled labor hours.

Product X requires 3 hours of machine time and 6 hours of skilled labor time. Product Y requires 6 hours of machine time and 3 hours of skilled labor time. The selling price is $50 for X and $80 for Y while the variable cost per unit is $30 for X and $40 for Y. Machine capacity is only 160 hours per week and skilled labor time available is only 260 hours per week.

Required: Advice Beta Ltd on the profit-maximizing product mix. Round your answer to the lowest unit.

Note:

Please i need the solution like this way exactly or i will get zero marks :

Without taking into consideration the limiting factors, Total contribution ($) = 20X+12Y

The two resource constraints can be expressed as equations:

Machine hours: 3X + 6Y = 160 (1)

Skilled labor hours: 6X + 3Y = 260 (2)

Multiplying equation (2) by 2, gives: 12X + 6Y = 520 (3)

Subtracting equation (1) from equation (3) gives: 9 X = 360 and X = 40 units

Therefore 3 x 40 + 6Y = 160; 6Y = 160 -120 = 40 and Y = 6.66 or 6 units

The profit-maximizing mix is 40 X and 6 Y