Xb N X1 X2 X3 X4 b Z 1 0 U 0 20 320 X1 0 0 1 2 -1 8 X3 0 1 M 0 G 8 With X3 and X1 being the basic variables in the above tableau and The entries M, U,G in the tableau are unknown parameters. (a) Suppose the LP problem was a minimization problem, give the range of values of the unknown parameters, that would make the optimal cost be negative infinite (b) Suppose the problem was a maximization problem, give the range of values of the unknown parameters, that would make the current solution to be optimal. Hence state the optimal solution. (c) Suppose that it is a maximization problem and that U= -10, U-G= 0.5,explain why the current solution is feasible but not optimal. Hence proceed and determine the optimal solution.

2) Find the domain only for the following functions: V2x + 5 Vx -2 x + 3 2) у %3 3) у %3 1) y = х- 2х -8 2- x x+4 4х 5) У - x + 3/ 6) y = 4) y = 4 - Vx - 9 Vx? + 4x Vx + 2x – 15 4 M.Sc. Hussein S. Yassin

The State of Maryland is considering a requirement that for every ton of CO2 produced by out- of-state electricity producers, a permit costing $40 must be purchased. It takes approximately 0.5 tons of coal to make 1 MWh of electricity, and every 1 ton of coal produces 2.86 tons of CO2. Write out the linear variable cost function for a coal-fired power plant in Ohio selling electricity to Maryland utilities which includes the permit cost assuming that the current cost of coal is $150 a ton and that this coal fired plant has an annual fixed cost of $1,000,000. (You may use the variable q to denote quantity of electricity in MWh in the cost function.)

We found that the marketing research department for the company that manufactures and sells memory chips for miarocomputers established the following price-demand and revenue functions: Px)= 85-4x Price-demand function Rix) = xp(x) = x(85-4x) where px) is the wholesale price in dollars at which x million chips can be sold, and R(x) is in millions of dollars. Both functions have domain 15xs17. Revenue function (A) Which of the following is the graph of the revenue function? A. OB. Oc. S 10 15 20 400- 200- 200- 400- 05 10 15 20 20 -15 -10 6 O (B) Find the output that will produce the maximum revenue. million chips (Type an integer or a fraction. Simplify your answer.) What is the maximum revenue? million (Round to two decimal places.) (C) What is the wholesale price per chip that produces the maximum revenue? (Round to the nearest dollar.)

SAMAH MALL Store chain has bought out a competing grocery store chain. However, it now has too many stores in close proximity to each other in certain cities. In AMMAN the chain has 10 stores, and it does not want any stores closer than 2 km to each other. Following is a map showing the general proximity of the stores. Stores within 2 km of each other are circled. 1 5 In the above-mentioned problem, the linear objective function is: