Question

Gaermont Perfumes manufactures "Sensatez" and "Sentimiento" perfumes. Each pound of raw material is purchased at a price of $ 3 per pound. One hour of labor is required to process a pound of raw material and each pound that is processed yields 3 ounces of "Sense" and 4 ounces of "Feeling". The ounce of "Sensatez" sells for $ 7, while the ounce of "Sentimiento" sells for $ 6. Gaermont has the option to further process both perfumes and obtain "Sensibility Plus" and "Deep Feeling". Each ounce of "Sensatez" can be transformed into an ounce of "Sensatez Plus" (which sells for $ 18), but it requires 3 hours of labor and the process costs $ 4. Each ounce of "Sentiment" can be transformed into one ounce of "Sentiment Deep" (which retails for $ 14), but it requires 2 hours of labor and the process costs $ 4. Gaermont has 6,000 hours of labor and 4,000 pounds of raw material. Formulate a PL problem that allows Gaermont to maximize its profits and specify this maximum.

Answer 1

Conversion factor: 1 pound = 16 ounces

LP model is as follows:

Let S be the ounces of "Sense" perfume to be produced and sold

F be the ounces of "Feeling" perfume to be produced and sold

SP be the ounces of "Sense" perfume to be produced and transformed into "Sensibility Plus" and sold

DF be the ounces of "Feeling" perfume to be produced and transformed into "Deep Feeling" and sold

M be the pounds of raw material used

Max 7S+6F+(18-4)SP+(14-4)DF-3M

or,

Max 7S+6F+14SP+10DF-3M

s.t.

1M+3SP+2DF <= 6000  (total hours of labor used)

S+SP-3M = 0   (material used in producing Sense and Sensibility Plus)

F+DF-4M = 0 (material used in producing Feeling and Deep Feeling)

M <= 4000   (total pounds of material used)

S, SP, F, DF, M >= 0