Company XYZ wants to maximize the profit for two products A and B which are sold at $ 25 and $ 20 respectively. There are 1800 resource units available every day and product A requires 20 units while B requires 12 units. Both of these products require a production time of 4 minutes and total available working hours are 8 in a day. What should be the production quantity for each of the products to maximize profits.
(a) Write the objective function for this problem.
(b) What are the decision variables in this problem?
(c) What are the constraints (resource and time) in this problem?
(d) Fill in the blank. Find optimal values for units of Product A and B to obtain the maximum sales within the given constraints.
You may use any method (R, Excel, anything else) to solve this problem; you do not have to show any code, however please show any equations/formulas you use or derive to support your thought process.
Company XYZ should produce __________ units of Product A, and ___________ units of Product B to get sales of ___________ dollars, which is the maximum sales the company can receive given the constraints.