(a) What basic feasible solution does this tableau represent? Is this solution optimal? Why or why not? (b) Does this tableau represent a unique optimum? If not, find an alternative optimal solution.

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Based on the following sensitivity analysis, which of the following products would be considered most sensitive to changes or errors in the objective function coefficient? A. Product_2 B. Product_1 C. Product_3   Variable Cells Cell Name Final Value Reduced Cost  Objective Coefficient AllowableIncrease AllowableDecrease $B$2 Product_1 0 −2 25 13 5 $B$3 Product_2 175 0 25 8 9 $B$4 Product_3 0 −1.5 25 11 3   Constraints Cell Name Final Value Shadow Price  Constraint R.H.Side AllowableIncrease AllowableDecrease $H$9 Resource_A 0 0 100 1E+30 100 $H$10 Resource_B 525 0 800 1E+30 275 $H$11 Resource_C 700 1.75 700 366.6666667 700

Find the point of intersection of the pair of straight lines. y  =  −7x  −  10 −y  =  8x  +  2 (x, y) =

For a copper-silver alloy of composition 62wt%Ag-38wt%Cu and at 775°C(1425°F) (see Animated Figure 9.7) do the following: (a) Determine the mass fractions of α and β phases. Mass fraction α= Mass fraction β= (b) Determine the mass fractions of primary α and eutectic microconstituents. Mass fraction α primary =____ Mass fraction eutectic =___ (c) Determine the mass fraction of eutectic α. Mass fraction α eutectic =_____

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-For this problem clearly derive the Linear program-Graph this problem and clearly indicate the feasible options- Clearly determine the solution to the problem using the method of points (be smart about which points you have to evaluate based on the graph of the objective function

A regression analysis between sales (in $1000s) and price (in dollars) resulted in the following equation: ​  = 50,000 − 8x ​ The above equation implies that an increase of _____.   a. $8 in price is associated with an increase of $8,000 in sales   b. $1 in price is associated with a decrease of $42,000 in sales   c. $1 in price is associated with a decrease of $8 in sales   d. $1 in price is associated with a decrease of $8,000 in sales

Prove the following using strong induction. Suppose you are gifted a collection of 3n pokéballs; all of the the pokéballs have the same size and weight except for one which is slightly heavier, and otherwiselook and feel exactly the same as the others. You are tasked with identifying theheavy pokéball and have at your disposal a set of balancing scales which can be usedto compare the weights of two collections of pokéballs. The scales can show whetherthe two collections have the same weight, or can show which collection is heavier if theweights are different. Prove using strong induction that you can identify the heavypokéball out of 3n pokéballs using n weighing operations.

Suppose your total benefits of renting x DVD's next month is: -²2² +14x+50 The cost of renting a DVD is $2, and so the total cost of renting x DVD's is $2x. Calculate your net benefit from watching 1, 2...8 DVDs. Complete column (2). (Enter your responses as integers.) (1) DVDs Rented 0 1 N345678 2 (2) Total Net Benefit