Homework SourseThe Texas Poker Company assembles three different poker sets
The Texas Poker Company assembles three different poker sets. Each Royal Flush (R) poker set contains 1000 poker chips, 4 decks of cards, 10 dice, and 2 dealer buttons. Each Deluxe Diamond (D) poker set contains 600 poker chips, 2 decks of cards, 5 dice, and one dealer button. The Full House poker (H) set contains 301 poker chips, 3 decks of cards, 3 dice, and one dealer button. The Texas Poker Company has 2,800,000 poker chips, 10,000 decks of cards, 25,000 dice, and 6000 dealer buttons in stock. They earn a profit of $38 for each Royal Flush poker set, $22 for each Deluxe Diamond poker set, and $12 for each Full House poker set. How many of each type of poker set (NR, ND, and NF) should they assemble to maximize profit? What is the maximum profit (p)?
Solution
Let the no. of sets of
Royal Flush = X1
Deluxe Diamond = X2
Full House = X3
From the details given in the question,
We have to maximixe profit, say Z, which is given by
Z = 38X1 + 22X2 + 12X3
We have the following constraints that are to be satisfied (using the data given in the question)
1000X1 + 600X2 + 301X3 <= 2,800,000 ..........................Eq1
4X1 + 2X2 + 3X3 <= 10,000 ...........................................Eq2
10X1 + 5X2 + 3X3 <= 25,000 .........................................Eq3
2X1 + X2 + X3 <= 6,000 ................................................Eq4
Note that the coefficients of X1, X2, X3 in Eq1,2,3,4, are the No.of Poker Chips, No.of Card Decks, No.of Dice, and No.of Dealer Buttons respectively. Also the values of X1, X2, X3 has to be a positive integer, as a set cannot be sold by parts.
The above formulated problem of equations is to be solved by Integer Programming. Solving the above problem manually is a very labourious work which can take several hours, incorporating several errors. I highly recommend that you use a Linear Programming Software to solve it. After solving, you get the following results:
No.of sets that are to be sold of each type are as follows:
Royal Flush = X1 = 1000
Deluxe Diamond = X2 = 3000
Full House = X3 = 0
Selling the above combination. we get maximum profit of Z = $104,000
