QUANTITATIVE METHODS (BCPC 208)
GROUP ASSIGNMENT ONE \( (22 / 4 / 2024) \)
NOTE:
1. To be completed, TYPED, and submitted in class on \( 8^{\text {th }} \) May, 2024.
2. Groups with very similar works will share a proportion of the marks!
3. Group numbers have been assigned; State your group number.
Question 1
A small mineral refinery manufactures two jewelry products namely necklaces and bracelets from gold, platinum and titanium. The refinery requires 9 and 3 ounces of gold to produce each necklace and bracelet respectively. In addition, each necklace requires 5 and 6 ounces of titanium and platinum respectively. The factory has a total of 240 and 275 ounces of platinum and titanium respectively. To make each bracelet stronger, the factory adds 4 and 5 ounces of platinum and titanium respectively, to the ounces of gold required. The firm has procured only 270 ounces of gold from a gold trader. In all, it costs the firm 415 and 455 to produce a bracelet and a necklace respectively, while a necklace is sold at 560 and a bracelet at 515. The firm wants to determine the number of necklaces and bracelets to make in order to attain the highest profit.
(i) Formulate a linear programming model for the above production problem
(ii) Using graphical analysis, find how many necklaces and bracelets the firm should produce and the largest profit from this production
(iii) Determine the shadow prices of each constraint
SIRR GODWILL
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