Problem #3. The Fruit-and-Nut Company wants to enter the snack mix market. It wants to introduce three types of mixes : (a) Standard mix. (2) Deluxe mix, and (3) Super- deluxe mix. Three raw materials are used in making each of the mixes. The Standard mix requires 1 pound of dry fruit, 2 pounds of nuts and 0.27 pounds of special ingredients. Similarly, the deluxe mix requires 2 pounds of dry fruit, 3 pounds of nuts, and 0.53 pounds of special ingredients. The Super-deluxe mix requires 2 pounds of dry fruit, 4 pounds of nuts and 0.46 pounds of special ingredients. The company has 5700 pounds of dry fruit, 7300 pound of nuts and 1900 pounds of special ingredients. They have already contracted to supply 350 pounds of Deluxe mix to a local shop. Marketing studies have indicated that they can sell at most 500 pounds of Super-deluxe mix. The profit from a pound of the Standard mix is $4.8. $6.4 from a pound of Deluxe mix, and $5.3 from a pound of Super-deluxe mix. Formulate the problem as an LP and answer the following questions. (Assume X1, X2, X3 represent the production quantities of Standard, Deluxe, and Super-deluxe mixes respectively.) (16) The number of less-than-or-equal-to type constraints (i.e., these constraints involve two or more variables and do not include the lower or upper bound conditions) in the formulation is equal to: (a) 0 _(b) 1 (c) 2 (d) 3 (e) none of the above (17) The number of greater-than-or-equal-to type constraints (i.e., these constraints involve two or more variables and do not include the lower or upper bound conditions) in the formulation is equal to: (a) 0 _(b) 1 (c) 2 (d) 3 (e) none of the above (18) Which of the following is a valid constraint? (a) 1X1 + 2X2 - 2x3 = 5700 _(b) 1X1 + 2X2 + 2X3 3 5700 (c) 1X1 + 2X2 + 0.27X3 5700 (e) none of the above (19) Which of the following is a valid constraint? a. 2X1 + 3X2 + 4x3 S 7300 (b) 2X1 + 3X2 +0.53X3 7300 (d) 2X1 + 3X2 -0.53X3 = 7300 (e) none of the above (20) Which of the following is a valid constraint? (a) 0.27X1 +0.53X2 +0.46X3 > 1900 (b) 0.27X1 + 3X2 + 2x3 = 1900 (c) 0.27X1 +0.53X2 +0.46X3 = 1900 _(d) 0.27X1 -0.53X2 +0.53X3 = 1900 (e) none of the above (21) The upper bound condition X3 350 is a part of the formulation. (a) True_(b) False (c) Not enough information (d) Irrelevant (23) The lower bound condition X2 > 350 is a part of the formulation. (a) True_(b) False (c) Not enough information (d) Irrelevant (24) The upper bound condition X1