A company assembles three different poker sets. Each Royal Flush poker set contains 1000 poker chips, 10 decks of cards, 4 dice, and 2 dealer buttons. Each DeluxeDiamond poker set contains 600 poker chips, 5 decks of cards, 2 dice, and one dealer button. The Full House poker set contains 300 poker chips, 5 decks of cards, 2dice, and one dealer button. The company has 2,900,000 poker chips, 25,000 decks of cards, 10,0000 dice, and 6500 dealer buttons in stock. They earn a profit of $38for each Royal Flush poker set, $22 for each Deluxe Diamond poker set, and $12 for each Full House poker set. Use the simplex method to complete parts (a) and (b)......(a) How many of each type of poker set should the company assemble to maximize profit? What is the maximum profit?Begin by finding the objective function. Let x1, x2, and x3 be the numbers of Royal Flush, Deluxe Diamond, and Full House poker sets, respectively. What is theobjective function?z= 38 x1 + 22 x2 + 12 x3(Do not include the $ symbol in your answers.)To maximize profit, the company should assemble 500 Royal Flush poker sets, 4000 Deluxe Diamond poker sets, and 0 Full House poker sets.(Simplify your answers.)The maximum profit is $ 107000 .(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 the answerbox(es) to complete your choice.(Simplify your answers.)А.decks of cards anddice remain unused in the optimal solution.В.dealer buttons remain unused in the optimal solution.С.dice remain unused in the optimal solution.D.poker chips,dice, anddealer buttons remain unused in the optimal solution. A company sells sets of kitchen knives. A Basic Set consists of 2 utility knives and 1 chef's knife. A Regular Set consists of 2 utility knives, 1 chef's knife, and 1 slicer. ADeluxe Set consists of 3 utility knives, 1 chef's knife, and 1 slicer. The profit is $40 on a Basic Set, $60 on a Regular Set, and $80 on a Deluxe Set. The factory has onhand 800 utility knives, 400 chef's knives, and 200 slicers.(a) If all sets will be sold, how many of each type should be made up in order to maximize profit? What is the maximum profit?(b) A consultant for the company notes that more profit is made on a Regular Set than on a Basic Set, yet the result from part (a) recommends making up more BasicSets than Regular Sets. She is puzzled how this can be the best solution. How would you respond?.....(a) Find the objective function to be used to maximize profit. Let x, be the number of Basic Sets, let X, be the number of Regular Sets, and let x, be the number ofDeluxe Sets.What is the objective function?z= 40 x1 + 60 x2 + 80 x3(Do not include the $ symbol in your answers.)(a) To maximize profit, the company should make up 100 Basic Sets, 0 Regular Sets, and 200 Deluxe Sets.(Simplify your answers.)The maximum profit is $ 20000 .(Simplify your answer.)(b) Choose the correct answer below.A. The overall profit is most affected by the Deluxe Set. The profit generated by the Basic Set and Regular Set does not significantly contribute to the overallprofit.B. The Basic Set requires fewer knives. So, fewer Basic Sets can be made up than Regular Sets. This results in higher overall profit.C. Since the Regular Set requires more knives, it has higher production costs. This will result in less profit than the Basic Set.D. The Basic Set requires fewer knives. So, more Basic Sets can be made up than Regular Sets. This results in higher overall profit.

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