A company makes three types of candy and packages them in three assortments. Ass

Question

A company makes three types of candy and packages them in three assortments. Assortment I contains 4 cherry, 4 lemon, and 12 lime candies, and sells for a profit of 00, Assortment II contains 12 cherry, 4 lemon, and 4 lime candies, and sells for a profit of $3.00. Assortment II contains 8 cherry, 8 lemon, and 8 lime candies, and sells for a profit of $5.00. They can make 4.800 cherry, 3, 800 lemon, and 5, 600 lime candies weekly. How many boxes of each type should the company produce each week in order to maximize its profit (assuming that all boxes produced can be sold)? What is the maximum profit? Select the correct choice below and fill in any answer boxes within your choice. A. The maximum profit is $ when boxes of assortment I, boxes of assortment and boxes of assortment are produced. B. There is no way for the company to maximize its profit.

Explanation / Answer

Let x be the number of assortment I items sold

Let y be the number of assortment II items sold

Let z be the number of assortment III items sold

profits earned is represented in eqaution

maximise f= 4x+ 3y +5z

now

The constraint equations are listed below:

4x + 12y + 8z 4800 (sour candy)

4x + 4y + 8z   3800     (lemon candy)

12x + 4y + 8z 5600     (lime candy)

x 0

y 0

z 0

This system can be solved using the Simplex method:

initial simplex tableau:

     x     y     z     s1    s2    s3    n

     4    12    8     1      0     0    4800

     4      4    8     0      1     0    3800

    12     4    8     0      0     1    5600

    -4    -3   -5     0      0     0         0

x1=125, x2=300, x0=225

The maximum profit of $2775 is obtained by selling 225 units of assortment I, 125 units of assortment II, and 300 units of assortment III.

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