An electronics firm produces two models of pocket calculators: the A-100 (A), wh
ID: 454418 • Letter: A
Question
An electronics firm produces two models of pocket calculators: the A-100 (A), which is an inexpensive four-function calculator, and the B-200 (B), which also features square root and percent functions. Each model uses one (the same) circuit board, of which there are only 2,500 available for this week's production. Also, the company has allocated a maximum of 800 hours of assembly time this week for producing these calculators, of which the A-100 requires 15 minutes (.25 hours) each, and the B-200 requires 30 minutes (.5 hours) each to produce. The firm forecasts that it could sell a maximum of 4,000 A-100's this week and a maximum of 1,000 B-200's. Profits for the A-100 are $1.00 each, and profits for the B-200 are $4.00 each.
What is the objective function?
What is the assembly time constraint (in hours)?
Which of the following is not a feasible production/sales combination?
What are optimal weekly profits?
Please show how to solve step by step. Thank you
Explanation / Answer
The Objective function has to be maximization of Profit. In case we define our decision variables as A( -number of A-100) and B (- number of B-200) to be produced then the objective of maximization of Profit is given as :
Maximize Z = A + 4B
Constraint in terms of hours available is : .25A + .5B <=(less than equal) 800
Constraint availability of circuit boards is : A + B <= 2500
Demand constraints are : A <= 4,000 and B <= 1000
Problem is linear programming having two variables, can be solved either using graphical method or simplex method ot using excel solver. Solution using excel solver is as follows:
Optimal solution is to Produce 1200 units of A-100 and 1000 (maximum demand) units of B-200 and earn maximum profit of $5,200
Decision Variables A B SumProd. Values 1200 1000 Objective function 1 4 5200 Constraints: RHS Circuit boards 1 1 2200 "<= 2500 Hours available 0.25 0.5 800 "<= 800 Maximum demand A 1 0 1200 "<= 4000 Maximum demand B 0 1 1000 "<= 1000Related Questions
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