A poker company assembles three different poker sets Each Royal Flush poker set

Question

A poker company assembles three different poker sets Each Royal Flush poker set contains 1000 poker chips, 4 decks of cards, 10 dice, and 2 dealer buttons Each Deluxe Diamond poker set contains 600 poker chips, 2 decks of cards, 5 dice, and one dealer button. The Full House poker set contains 300 poker chips, 2 decks of cards, 5 dice, and one dealer button. The 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. Complete parts (a) and (b) below. (a) How many of each type of poker set should they assemble to maximize profit? What is the maximum profit? Begin by finding the objective function. Let x_1 be the number of Royal Flush poker sets, let x_2 be the number of Deluxe Diamond poker sets, and let x_3 be the number of Full House poker sets. What is the objective function? z = x_1 x_2 + x_3 (Do not include the symbol in your answers.) How many of each type of poker set should they assemble to maximize profit? What is the maximum profit? The company should produce Royal Flush poker sets, Deluxe Diamond poker sets, and Full House poker sets. (Simplify your answers, ) What is the maximum profit? $ (b) Find the values of any nonzero slack variables and describe what they tell you about any unused components. Select the correct choice below and fill in any answer boxes within your choice. (Simplify your answers.) A. s_3 = means that this many dice remain. Click to select your answer(s).

Explanation / Answer

We max profit as : z = 38x1+22x2+12x3, subject to

1000x1+600x2+300x3<=2800000, 10x1+6x2+3x3<=28000

4x1+2x2+2x3 <=10000, 2x1+x2+x3<=5000

10x1+5x2+5x3<=25000, 2x1+x2+x2<=5000

2x1+x2+x3<=6000

From above 4 constraints, we can simplify them to get the following constraints:

10x1+6x2+3x3<=28000

2x1+x2+x3<=5000

and x1,x2,x3>=0

Solving this we get:

x1=1000,x2=3000,x3=0

Profit = $104000

Used poker chips = 1000*1000+3000*600 = 2800000, hence completely used

Used decks = 4*1000+2*3000 = 10000, completely used

Used dice = 10*1000+5*3000 = 25000, completely used

SO, 0 dice remain

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.