X-Tech Inc. produces specialized bolts for the aerospace industry. The operating cost of producing a single bolt is $2.

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X-Tech Inc. produces specialized bolts for the aerospace
industry. The operating cost of producing a single bolt is $2. The
company currently sells the bolts for $6/unit. Each time the
company arranges to sell a batch, it incurs a fixed cost of $20.
This fixed cost mainly includes administrative expenses. The volume
of sales is primarily dependent on the price of the product. The
manager has come up with the following relationship between demand
(volume) and price: Volume = 500 – 25*price.
Determine the optimal price and optimal volume that will result
in the maximum profit. Solve the problem using Excel solver.
Due to marketing and competitive considerations, X-Tech decided
to limit its price to $8. State the non-linear programming
formulation of this problem, and solve it.
Repeat part b by changing the restriction on price from a
maximum of $8 to a maximum of $14.