McNaughton Inc. produces twin steak sauces, Spicy Diablo and mild Red Baron. These sauces are both made by blending two ingredients, A and B. A certain level of flexibility is permitted in the formulas for these products. The allowable percentages, along with revenue and cost data, are given in the following table. Up to 40 quarts of A and 30 quarts of B could be purchased. McNaughton can sell as much of these sauces as it produces.

Formulate a LP with the objective to maximize net profit from the sale of the sauces.

Sauce	Ingredient		Sales Price per Quart
	A	B
Spicy Diablo	At least 25%	At least 50%	3.35
Red Baron	At most 75%	none	2.85
Cost per Quart	$1.60	$2.59

Answer:

This is related and can be expressed in therms of Linear Programming;  a mathematical optimization technique concerned typically with allocation of scarce (limited) resources. It is a procedure to optimize the value of some linear objective function when the factors involved are subject to some constraints expressed as linear inequalities and/or equalities.

LP problem in standard form = Objective Function + Constraints (Limitations)

Objective function = linear function of decision variables called also activities. It represents the results required (typically: maximize profit, minimize costs).

Constraints (Limitations) = quantified restrictions expressed
mathematically by linear inequalities. Typical constraints are: Maximizing problems: Minimizing problems:

Here in the above problem also :

Assume :

D = quarts of Diablo to be produced

R = quarts of Red Baron to be produced

AD= quarts of A used to make Diablo

AR = quarts of A used to make Red Baron

BD = quarts of B used to make Diablo

BR = quarts of B used to make Red Baron

CONDITIONS GIVEN :

MAX 3.35 D + 2.85 R - 1.6 AD - 1.6 AR - 2.05 BD - 2.05 BR
ST 2) - D + AD + BD = 0
3) - R + AR + BR = 0
4) AD + AR <= 40
5) BD + BR <= 30
6) - 0.25 D + AD >= 0
7) - 0.5 D + BD >= 0
8) - 0.75 R + AR <= 0

END OBJECTIVE FUNCTION VALUE 1) 99.0000000