A coffee merchant sells two blends of coffee. Each pound of blend A contains 80%

Question

A coffee merchant sells two blends of coffee. Each pound of blend A contains 80% Mocha Java and 20% Jamaican and sells for $2 a pound. Each pound of blend B contains 35% Mocha Java and 65% Jamaican and sells for $2.25 a pound. The merchant will try to sell the amount of each blend that maximizes her income. Let X be the number of pounds of blend A and Y be the number of pounds of blend B.

Objective:

A.) Find the objective function

B.) Since the merchant above has available 1000 pounds of Mocha Java, what is the constraint that must be satisfied?

C.) Since the merchant above has available 600 pounds of Jamaican, what is constraint that must be satisfied?

Explanation / Answer

Answer A:

If the merchant sells X kg of the first blend then profit from the first blend is 2X, and

if he sells Y kg of the second blend then profit from the second blend is 2.25Y.

Therefore the objective function will be 2X + 2.25Y.

Answer B:

If the merchant has only 1000 pounds of Mocha Java, then the total Mocha availble for sale can be given by:

0.8X + 0.35Y =< 1000.

This is the required constarint that must be satisfied.

Answer C:

If the merchant has only 1000 pounds of Mocha Java, then the total Mocha availble for sale can be given by:

0.2X + 0.65Y =< 600.

This is the required constarint that must be satisfied.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.