Solve the following linear programming problems graphically.

Question

San Gabriel corporation produces both soda and juice drinks. A case of soda requires 2 pounds of malt and 3 pounds of sugar while a case of juice requires 1 pound of malt and 4 pounds of sugar. During a given week, San Gabriel Corp has 160 pounds of malt and 340 pounds of sugar available. It the profit for each soda and juice is Php 30 per case, how many cases of soda and juice drinks should the company produce each week?

Answer 1

Well suppose you produce x cases of soda and y of juice.

Then

x >= 0

y >= 0

Malt constraint : 2x + y <= 160

Sugar constraint : 3x + 4y <= 340

Profit = 30 (x+y).

So graphically.

On Desmos plot the feasible region, bounded by

x=0

y=0

2x+y = 160

3x+4y = 340

On your graph find the vertices of this region

At each vertex find (x,y) and calculate 30 (x+y)

Choose the vertex with the highest value of 30 (x+y)

That gives you the required number of cases