Question

A producer will supply 30 items at a price of $15 per item. For every $9 increase in price per item, 595 more items will be provided
Find the linear supply function, p(x), for this item. Enter your answer in slope-intercept form, using exact numbers. (use p for p(x).)

Answer 1

From the information given about the producer, the linear supply function will be p = 94.17x + 1382.55.

How to solve the linear supply function

The equation of the linear supply is given as mx + c.

From the information given, the equation will be:

30 = (15 × m) + c

30 = 15m + c

Also, the second equation will be:

595 = (21 × m) + c

595 = 21m + c

Subtract equation i from ii.

(595 - 30) = 21m - 15m

565 = 6m

m = 565/6 = 94.17

Therefore, we will put the value of m into the equation. This will be:

30 = 15m + c

30 = (15 × 94.17) + c

30 = 1412.55 + c

c = 1412.55 - 30

c = 1382.55

Therefore, the equation will be p = 94.17x + 1382.55.

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