I don't even know where to start

Question

a company makes $25 profit from the sales of a product A and $35 from product B. Each uses 3 units of material and 5 units of labor. Each B requires 5 units of material and 4 units of labor. Let x be the number of A to manufacture and y the number of B. Write the objective function and all the constraints necessary to maximize profit if the company has only 300 units of material and 400 units of labor available. DO NOT SOLVE

Answer 1

300m, 400L available to use

A requires 3m and 5L which makes $25 profit

B requires 5m and 4L which makes $35 profit

x= number of A produced, y=number of B produced

write the objective function to maximize profits and the constraints

25x+ 35y - ((3m+5L)x + (5m+4L)y) = profit

(25-3m-5L)x + (35-5m-4L)y = profit= objective function to be maximized

constraints are (3m+5m)x </= 300, 8mx </=300m, x = 300m/8m = 75/2= 37.5 of A

and (5L +4L)y </= 400, 9Ly</=400L, y = 400/9 = 44 4/9 of B

and L,m>/=0

check the vertices of the quadrilateral outlined by the constraint lines, to find which maximizes profit

(0,0), (0,44 4/9), (37 1/2, 0), (37.5, 44 4/9)