Please use EXCEL TO SOLVE this question. GE Manufactures several products: 55-in
ID: 3178232 • Letter: P
Question
Please use EXCEL TO SOLVE this question.
GE Manufactures several products: 55-in GE55 and 65-in GE65 TVs. It makes a profit of $50 on each GE55 and $75 on each GE65 TVs manufactured. During each shift, GE allocates up to 300 man-hours in its production area and 240 man-hours in assembly area to manufacture the TVs. Each GE55 requires two man-hours in the production area and one man-hour in the assembly area, whereas each GE65 requires two man-hours in the production area and three man-hours in the assembly area.
i How many decision variables do you need to solve this problem?
ii. Write down the decision variables.
iii.Set up the Objective function. The Objective function has to be ______________
iv. Write down the constraints.
a. What production levels of GE55 and GE65 TV sets optimize the expected profit per shift?
What is the optimal expected profit per shift?
b. What is the shadow price for extra assembly hours? Interpret.
c. Would the optimal solution change if the unit profit for GE65 TVs were increased to (i) $135? (ii) $300?
Explanation / Answer
i) and ii)
There are two decision variables are required to solve this problem.
let x be the number of 55 in GE55 adn y be the number of 65 in G65
iii)
Objective function is to maximize the profit
Maximize Z = 50x + 75y
iv)
Constraints are
2x + 2y <= 300
x + 3y <= 240
(A)
Solving this linear problem gives the optimal production level for both variants
105 number of GE55 TVs
45 number of GE65 TVs
This gives the maximum profit of $8625.
(B)
Shadow price of assembly hours is $12.5