To find the optimal solution to a linear programming problem using the graphical method a. find the feasible point that is the farthest away from the origin. b. find the feasible point that is at the highest location. c. find the feasible point that is closest to the origin. d. None of the alternatives is correct. Let xij = the production of product i in period j. To specify that production of product 1 in period 3 and in period 4 differs by no more than 100 units, which of the following constraints are correct? P13 - P14 <  100;   P14 - P13  <  100 (a) P13 - P14 <  100;   P13 - P14  >  100 (b) P13 - P14 <  100;   P14 - P13  >  100 (c) P13 - P14 >  100;   P14 - P13  >  100 (d) 3. Whenever all the constraints in a linear program are expressed as equalities, the linear program is said to be written in a. standard form. b. bounded form. c. feasible form. d. alternative form.

North Dakota Electric Company estimates its demand trend line (in millions of kilowatt hours) to be: D = 77.0 +0.43Q, where Q refers to the sequential quarter number and Q = 1 for winter of Year 1. In addition, the multiplicative seasonal factors are as follows: Quarter Winter Spring Summer Fall In year 26 (quarters 101-104), the energy use for each of the quarters beginning with winter is (round your response to one decimal place): Quarter Winter Factor (Index) 0.80 1.20 1.40 0.60 Spring Summer Fall Energy Use

1 1 4. Given the production function f(L,K) = K³L³, find the long-run cost minimizing input combination L and K as functions of q, w and r, where q is the output level the firm is producing. Write the cost function.

“Good Intentions” (GI) company produces two products, which it sells on both a cash and credit basis. Revenues from credit sales will not have been received but are included in determining profit earned during the current six-month period. Sales during the next six months can be made either from units produced during the next six months or from the beginning inventory. Relevant information about products one and two is as follows. During the next six months, at most 150 units of product type 1 can be sold on a cash basis, and at most 100 units of product 1 can be sold on a credit basis. It costs £35 to produce each unit of product type 1, and each sells for £40. A credit sale of a unit of product 1 yields £0.50 less profit than a cash sale (because of delays in receiving payment). Two hours of production time are needed to produce each unit of product 1. At the beginning of the six-month period, 60 units of product 1 are in the inventory. During the next six months, at most 175 units…