A company manufactures two different sets of collectible tin toy robots, A and B. Both of them have to go through two production processes, I and 2. The corresponding labor time (min/unit) required for each production process is given as below :

A B Available times

Process 1 (min/unit) 25 30 3,000 minutes/week

Process 2 (min/unit) 50 20 4,000 minutes/week

Profit ($/unit) 205 410 -

Since robot B targets professional toy collectors, each item has to go through a final delicate painting process for two minutes and the available time is 150 minutes / week. In addition, since the supply of a particular part used in robot A is currently tight, the maximum number of sets of A to be produced per week is 70.

a. Formulate a linear programming model algebraically for the above problem to determine the optimal number of sets of the two robots to be produced per week so as to maximize total profit. Use the graphical method to solve this model.

b. Use the Excel Solver to solve this model.

(For part (b), in addition to your written answers, you have to submit the relevant. Excel spreadsheet in which the problem is properly formulated with the optimal solution obtained by the Solver.)

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