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?
A)Z = $4.00 A + $1.00 B
B)Z = $0.25 A + $1.00 B
C)Z = $1.00 A + $4.00 B
D)Z = $1.00 A + $1.00 B
E)Z = $0.25 A + $0.50 B

Question

Quizplus · Accepted Answer

The objective function represents the total profit that the company can make by producing the calculators. Since the profit for A-100 is $1.00 and for B-200 is $4.00, the objective function can be represented as follows: 
Z = $1.00 A + $4.00 B 
where A represents the number of A-100 calculators produced and B represents the number of B-200 calculators produced.

The company has limited resources, which are the circuit boards and assembly time. To produce one A-100 calculator, the company needs 15 minutes of assembly time, whereas to produce one B-200 calculator, it needs 30 minutes of assembly time. Therefore, the total assembly time required can be represented as: 
0.25A + 0.50B ≤ 800

Similarly, there are only 2500 circuit boards available for this week's production, and each calculator model requires only one circuit board, so the total number of calculators that can be produced is limited by the number of circuit boards available. Therefore, the total number of calculators produced can be represented as: 
A + B ≤ 2500

Also, the company has forecasted the maximum number of calculators that it can sell, which are 4000 A-100 and 1000 B-200. Therefore, the total number of calculators produced cannot exceed the maximum number that can be sold. Therefore, the total number of calculators produced can be represented as: 
A ≤ 4000 
B ≤ 1000

Therefore, the problem can be formulated as follows:

Maximize Z = $1.00 A + $4.00 B 
subject to: 
0.25A + 0.50B ≤ 800 
A + B ≤ 2500 
A ≤ 4000 
B ≤ 1000

Solving this linear programming problem will give us the optimal values for A and B that maximize the total profit. The solution to this problem is A = 2500, B = 0, which means that the company should produce only A-100 calculators and no B-200 calculators to maximize its profit. Therefore, the best choice is C.

An Electronics Firm Produces Two Models of Pocket Calculators: the A-100