Cost Minimization
Ray Barone is sole proprietor of Delmar Custom Homes (DCH), a family- run construction company. The company uses two types of crews on its Long Island, New York, home construction projects. Type A crews consist of master carpenters and skilled carpenters, whereas B crews include skilled carpenters and unskilled labor. Each home involves framing (F), roofing (R), and finish carpentry (FC). During recent months, A crews have demonstrated a capability of framing one home, roofing two, and doing finish carpentry for no more than four homes per month. Capabilities for B crews are framing three homes, roofing two, and complet- ing finish carpentry for one during a month. DCH has agreed to build 10 homes during the month of July but has subcontracted 10% of framing and 20% of finish carpentry requirements. Labor costs are $60,000 per month for A crews and $45,000 per month for B crews.
A. Formulate the linear programming problem that DCH would use to minimize its total labor costs per month, showing both the inequality and equality forms of the constraint conditions.
B. Solve the linear programming problem and interpret your solution values.
C. Assuming that DCH can both buy and sell subcontracting services at prevailing prices of $8,000 per unit for framing and $14,000 per unit for finish carpentry, would you recommend that the company alter its subcontracting policy? If so, how much could the company save through such a change?
D. Calculate the minimum increase in A-crew costs necessary to cause DCH to change its optimal employment combination for July.