SOLUTION: Mountain Sales Bicycle Shop makes PhP100 on each Model X bike sold and PhP50 on each Model Y bike sold. The bike shop's overhead is PhP1500 per month. Each month the owner can get

Question 1185324: Mountain Sales Bicycle Shop makes PhP100 on each Model X bike sold and PhP50 on each Model Y bike sold. The bike shop's overhead is PhP1500 per month. Each month the owner can get as many as 20 Model X bikes and 30 Model Y bikes. Also the maximum number of bikes which the shop can stock is 40. Find the number of Model X and Model Y bikes he must sell to maximise the profit. What is the profit?
linear programming
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

With only the one constraint (total number of bikes at most 40), this is not a particularly interesting linear programming problem. It is obvious that the maximum profit will be when the number of bikes of the style that produces the larger profit is as large as possible.

So the maximum profit is when the number of Model X bikes is 20, which means the number of Model Y bikes is 40-20=20.

The profit in PhP from selling the bikes is then

The overall profit is then that profit, minus the fixed overhead costs:

ANSWERS:
The maximum profit is when he sells 20 of each model during the month;
The amount of the profit is PhP1500

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