Statistics and Probability

loo Pivot once as indicated in the given simplex x1 x2 :3 s tableau. Read the solution from the result. ' ' (Simplify your answers.) Donna De Paul is raising money for the homeless. She discovers that each church group requires 2 hours of letter writing and 1 hour of follow-up, while for each labor union she needs 2 hours of letter writing and 3 hours of follow-up. Donna can raise $150 from each church group and $200 from each union local, and she has a maximum of 20 hours of letter writing and a maximum of 12 hours of follow-up available per month. Determine the most protable mixture of groups she should contact and the most money she can raise in a month. Let x1 be the number of church groups, and let x2 be the number of labor unions. What is the objective function? 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 2,700,000 poker chips. 10,000 decks of cards, 25,000 dice, and 6500 dealer buttons in stock. They earn a prot 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 prot? What is the maximum prot? Begin by nding the objective function. Let M be the number of Royal Flush poker sets, let x2 be the number of Deluxe Diamond poker sets. and let x3 be the number of Full House poker sets. What is the objective function? (h) Find the values of any nonzero slack variables and describe what they tell you about any unused components. A manufacturer of bicycles builds racing, touring, and mountain models. The bicycles are made of both steel and aluminum. The company has available 49,400 units of steel and 30,000 units of aluminum. The racing, touring, and mountain models need 13, 19, and 28 units of steel. and 12, 18, and 15 units of aluminum, respectively. Complete parts (a) through (d) below. (a) How many of each type of bicycle should be made in order to maximize prot if the company makes a; 8 per racing bike, 5 13 per touring bike, and $24 per mountain bike? Let x1 be the number of racing bikes, let x2 be the number touring bikes. and let x3 be the number of mountain bikes. What is the objective function? b) What is the maximum possible prot? To nd the maximum possible prot, read the value of z from the simplex tableau for the optimal solution