Jalal Kamal and Ahmad Bdair own and operate Jalal & Ahmad, Inc., a Hebron- based installer of conversion packages for vans manufactured by the major auto companies. Jalal & Ahmad hasfixed capital and labor expenses (FC)of $1.2 million per year, andvariable materials expensesaverage(AVC)$2,000 per van conversion. Recent operating experience suggests the followingannual demand relationfor Jalal & Ahmad products:

Q = 1,000-0.1P

where Q is the number of van conversions (output) and P is price.

(A)CalculateJalal & Ahmad'sprofit-maximizing output, price, and profit levels. Do not forget todemonstrate that profit is maximized at the level of output.

(B)Using theLagrangian multiplier method, calculateprofit-maximizing output, price, and profit levelsin light of aparts shortage that limits Jalal & Ahmad's outputto 300 conversions during the coming year.

(C)Calculate and interpret, the Lagrangian multiplier.

(D)Calculate the valueto Jalal & Ahmadof having the parts shortageeliminated.