can anyone help with this optimisation problem?

[jib jib]

there is a clothing company that makes a up market line and a budget line of clothing using 3 materials:
the up-market line = 50%A + 20%B + 30%C
the budget line = 20%A + 50%B + 30%C
market price are $790/tonne for upmarket and $700 for the budget line.
For a period the company can by 100 metres of A for $800/metre, 100 metres of B for $600/metre and 75 metres of C for $400/metre.

first you have to calculate the profit per meter for each line. and then find out how much of each line the company should produce to maximise it's profit.

i just want help with the starting variables:
i've started to write:: (x1, x2 representing the 2 lines)
z=790[x1]+700[x2]-800(0.5[x1]+0.2[x2])-600(0.2[x1]+0.2[x2])-400(0.3[x1]+0.3[x2]

subject to
amount of A : 0.5[x1] + 0.2[x2] < 100
amount of B : 0.2[x1] + 0.5[x2] < 100
amount of C : 0.3[x1] + 0.3[x2] < 75

can anyone tell me if i'm on the right track? i don't know where to put the purchasing prices!!!

[Rassis]

I think tons make no sense. Tons must be replaced by meters. Being so, you have:

Profit(max):

Z = 790 - (0.5 x 800 + 0.2 x 600 + 0.3 x 400).X1 + 700 - (0.2 x 800 + 0.5 x 600 + 0.3 x 400).X2
Z = 150.X1 + 210.X2

Constraints:

0.5.X1 + 0.2.X2 <= 100
0.2.X1 + 0.5.X2 <= 100
0.3.X1 + 0.3.X2 <= 75
X1 >= 0
X2 >= 0

Solution: X1 = 83 m and X2 = 166 m with a profit of Z = $47,500

I attach an Excel file where the solution was obtained with SOLVER.

Good luck.

[jib jib]

thankyou!!!!! so helpful!!!