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Market research into demand for a product indicates that when the selling price per unit is $145, demand in each period will be 5,000 units and if the price is $120, demand will be 11,250 units. It is assumed that the demand function for this product is linear. The variable cost per unit is $27.
What selling price should be charged in order to maximize the monthly profit?
Answer is $96.
I’ve tried several times but ended up getting figures over $100. Please help Sir.
Thanks. ?
In the price demand equation, b = (145-120) / (11,250 – 5,000) = 0.004
a = 145 + (5,000 x 0.004) = 165
(or, alternatively, a = 120 + (11,250 x 0.004) = 165)Therefore, MR = 165 – (2 x 0.004)Q = 165 – 0.008Q
For maximum profit, MR = MC
So 165 – 0.008Q = 27
0.008Q = 138
Q = 138/0.008 = 17,250Putting Q = 17,250 in the price demand equation gives:
P = 165 – (0.004 x 17250) = $96
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