Question

A store makes ice milk and ice cream each day. Suppose that each quart of ice milk requires 0.4 quart of milk and 0.2 quart of cream, while each quart of ice cream requires 0.2 quart of milk and 0.4 quart of cream. Suppose also that the profit on each quart of ice milk is Php 8.00 and Php 10.00 profit on each quart of ice cream. If the store has 10 quarts of milk and 14 quarts of cream each day, how many quarts of ice cream and ice milk should be made each day to maximize the store’s profit?

(Linear Programming solution) with graphs and table

Answer 1

let the two typer be x dy Given x has profit 8 y hau profit 10 We have to maximize profit let it be z Z = 8x + loy milk cream 0.4x + 0-2y S10 0-2x + 0.41 & 14 xiy >o 0.48 + 0.9= 10 y intercept = 50 a intercept = 25 0-99 + 0.4 y = 14 yintercept = 35 a intercept = 10 4x + 2y = 100 - 0 2x + 4y = 140 - ① xq 44 +24 -100 40 +84 = 280 By - 180 y=30 4x + 960) = 100 ( by sub ino ) =107

25 to required region . Points are (25,50) ( 70,35) (10,30) substitute above points in 8x4104 8(25) + 10150) = 700 8170) + 10135) - 910 8(10) + 101307 - 380 Marimum value is 910 si Q = 70 d y = 35 ös Quarts of milk = 0.4(70) +0-2/35) = 35 .. Quarts of cream - 0.9(70) + 0.4(35) = 28