Daisy Drugs manufactures two drugs: 1 and 2. The drugs are produced by blending two chemicals: 1 and 2. By weight, drug 1 must contain at least 65% chemical 1, and drug 2 must contain at least 55% chemical 1. Drug 1 sells for $6/oz, and drug 2 sells for $4/oz. Chemicals 1 and 2 can be produced by one of two production processes. Running process 1 using 4 hours of skilled labor yields 3 oz of each chemical. Running process 2 using 3 hours of skilled labor yields 3 oz of chemical 1 and 1 oz of chemical 2. Atotal of 120 hours of skilled labor is available. Formulate an LP that can be used to maximize Daisy's sales revenue.

model winstP3_9_6 "P r oduc ti on P r o c e s s ( Daisy Drug ) ";

set

drug :=[ 1..2];

chemical :=[ 1..2];

process :=[ 1..2];

parameter

PercentReq{drug, chemical} := [0.65, 0, 0, 0.55];

Price{drug} := [6, 4];

LaborUse{process} := [2, 3];

RawMatUse{process} := [3, 2];

ChemicalYield{process, chemical} := [3, 3, 3, 1];

LaborAvail := 120;

RawMatAvail := 100;

variable

RunProcess,R{process};

Blend,B{chemical,drug};

constraint

LaborLimit: sum{process} LaborUse*R <= LaborAvail;

RawMatLimit: sum{process} RawMatUse*R <= RawMatAvail;

ChemBalance{chemical}: sum{process} ChemicalYield*R >= sum{drug} B;

RequireChem{drug,chemical|PercentReq>0}: B >= PercentReq*(sum{

chemical} B);

maximize TotalRevenue: sum{chemical,drug} Price*B;

Writep(TotalRevenue);

end

Step-by-step explanation:

The formulated LP (linear programming) model is shown in the answer section. In order to maximize the revenue sales, it is essential to consider all the necessary factors such as the constraints, variables, production cost, availability of customers and customers' preferences. These factors was used to design the LP model shown above.

step-by-step explanation:

y = | -2(-2) |     →     y = | 4 |     →     y = 4       ⇒   (-2, 4)

y = | -2(-1) |     →     y = | 2 |     →       y =   2       ⇒   (-1, 2)    

y = | -2(0) |     →     y = | 0 |     →       y = 0         ⇒   (0, 0)

y = | -2(1) |   c →     y = | -2 |     →     y =   2         ⇒   (1, 2)    

y = | -2(2) |     →     y = | - 4 |     →     y =   4         ⇒   (2, 4)