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I'm a bit lost in this problem.:

The Mom and Pop Ice Cream Company makes two kinds of chocolate ice cream: regular and premium. The properties of 1 gallon (gal) of each type are show in the table:

Type - Regular - Premium

Flavoring - 24 oz - 20 oz

Milk-fat products - 12 oz - 20 oz

Shipping weight - 5 lbs - 6 lbs

Profit - 0.75 cents - 0.90cents

In addition, current commitments require the company to make at least 1 gal of premium for every 4 gals of regular. Each day, the company has available 725 pounds (lb_ of flavoring and 425 lb of milk-fat products. If the company can ship no more than 3000 lb of product per day, how many gallons of each type should be produced daily to maximize profit?

What I have so far is (I'm not sure if it's correct! :( )

Let x be number of gallons of regular ice cream and

Let y be number of gallons of premium ice cream

Objective Function: M = 0.75x + 0.90y

Constraints:

x≥0

y≥0

24x+20y≤725

12x+20y≤425

5x+6y≤3000

I think I'm supposed to do something with that 1:4 ratio...when I try to get the x and y intercepts I get decimals/fractions.

(30.20,0)...(0,36.25)

(35.41,0)...(0,21.25)

(600,0)...(0,500)

Any help is appreciated. Thanks.

EDIT: Okay so my teacher said to convert the oz to lbs. Since 1 lb = 16 oz, I get the following intercepts:

(483.33,0)...(0,580)

(566.66,0)...(0,340)

(600,0)...(0,500)

How do I even plot that on a graph ?_?

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  • $\begingroup$ Notifying you of changes...well...additions. $\endgroup$ – icewolf461 Jul 29 '16 at 12:37
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Perhaps add another constraint $x - 4y \leq 0$?

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  • $\begingroup$ Yes, but I don't have enough reputation to post comments yet. -_- $\endgroup$ – harvey Jul 26 '16 at 18:51
  • $\begingroup$ Ahhh. That makes sense. Well, it passed my view in the "first posts" queue! $\endgroup$ – Namaste Jul 26 '16 at 18:57

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