You can
put this solution on YOUR website!SEE MY COMMENTS BELOW...
Hi, I need help solving this problem, I tried it, but I didn't get far.
The dairy is capable of producing a maximum of 600 gallons of ice cream each day.
Ingredients for regular brand ice cream cost $0.60 per gallon, and premium brand costs $1.50 per gallon. The company can spend no more than $675 per day on the ingredients.
Regular brand requires 4- person hours to produce 100 gallons of ice cream, whereas premium brand requires 4-(IS IT 5??) person hours to produce 100 gallons. The dairy is able to run 26 person hours per day of production.
Here's what I got: (p= premium, r= regular, P=profit)
Max number of gallons that can be produced each day:
p + r <= 600..................OK....................I
Cost of ingredients per gallon produced each day:
1.5p + .6r <= 675.....................OK.................II
Number of person hours to produce ice cream each day:
.04r + .05p <= 26.............OK...IF 5 HRS ARE NEEDED FOR PREMIUM BRAND....III
The question I'm having trouble with is: How many gallons of each brand of ice cream should the diary produce to maximize it's daily profit, taking into account all of the production requirements identified. Provide supporting work that clearly describes your solution.
I believe the equation would be:
P= (.6r) + (1.5p) - 675 (Is this right?)............NO...PROFIT IS OBTAINED BY DEDUCTING THE COST PRICE FROM SALE PRICE.HERE THIS DATA IS NOT GIVEN.HENCE WE NEED THAT DATA SAY SALE PRICE OF THE 2 BRANDS TO KNOW THE PROFIT AND THEN MAXIMISE THE PROFIT . SUPPOSE IT IS MENTIONED THAT NET PROFIT ON SALE OF REGULAR BRAND IS SAY X AND NET PROFITON ON SALE OF PREMIUM BRAND IS Y THEN
P=rX+pY...WHICH WE WILL MAXIMISE SUBJECT TO THE 3 COSTRAINTS GIVEN BY EQNS.I,II AND III.
But then again, how can I include the hours, or are they not necessary?
I need help finding the amount of gallons of each brand that will make the greatest profit.
