A company sells sets of kitchen knives. A Basic Set consists of 2 utility knives and 1 chef’s knife. A Regular Set consists of 2 utility knives, 1 chef’s knife, and 1 slicer. A Deluxe Set consists of 3 utility knives, 1 chef’s knife, and 1 slicer. The profit is $20 on a Basic Set, $40 on a Regular Set, and $80 on a Deluxe Set. The FACTORY has on hand 1600 utility knives, 800 chef’s knives, and 400 slicers.
(a) Find the objective function to be used to maximize profit. Let x 1×1 be the number of Basic Sets, let x 2×2 be the number of Regular Sets, and let x 3×3 be the number of Deluxe Sets.
(Simply write the objective function on your paper. Do not include the $ symbol in your answers. You are not allowed to enter your answer for the problem into MML.)
(b) If all sets will be sold, how many of each type should be made up in order to maximize profit? Use the simplex method to derive your answers.
All supporting written work showing how you derived your final answer using the simplex method for this portion of the problem should be shown on your paper, including your final answer. You must write the entire following statement (filling in the blanks with your answers) for your final answer on your paper. Failure to do will cause a point(s) reduction in your grade. You are not allowed to enter your answer for the problem into MML.
”To maximize profit, the company should make up _________ Basic Sets, ________ Regular Sets, and __________ Deluxe Sets.”
(c) What is the maximum profit?
All supporting written work showing how you derived your final answer for this portion of the problem should be shown on your paper, including your final answer. Failure to do will cause a point(s) reduction in your grade. You are not allowed to enter your answer for the problem into MML.
(Round your final answer to the nearest whole number. Your final answer must also include the unit(s) of measure.)
