Question

A local bagel shop produces two products: bagels (B) and croissants (C). Each bagel requires 6 ounces of flour, 1 gram of yeast, and 2 tablespoons of sugar. A croissant requires 3 ounces of flour, 1 gram of yeast, and 4 tablespoons of sugar. The company has 6,600 ounces of flour, 1,400 grams of yeast, and 4,800 tablespoons of sugar available for today's production run. Bagel profits are 20 cents each, and croissant profits are 30 cents each. What are optimal profits for today's production run?

Answer 1

Let

B = No. of bagels produced
C = No. of croissants produced

Maximize Z = total profit = 0.20 B + 0.30 C

Subject to,

6 B + 3 C <= 6600 (Flour)

1 B + 1 C <= 1400 (Yeast)

2 B + 4 C <= 4800 (Sugar)

B, C >= 0

Solution using graphical method

This is a maximization problem. The isoprofit line (objective function), moving away from the origin, leaves the feasibility region, finally at the point (400, 1000).

So, the optimal solution to this problem is as follows:

B = 400
C = 1000
Max. Profit = 400*0.2 + 1000*0.3 = $380