Labor fluctuating needs in construction projects can be met through hiring and end employment. Both activities incur cost. The goal is to minimize the total cost of acquiring needed labor force. A contractor estimates that the size of the workforce needed over the next 5 weeks is 5, 7, 8, 4, and 6 workers. Excess labor kept on the force will cost $300 per worker per week, and new hiring in any week will incur a fixed cost of $400 plus $200 per worker per week. Find the optimal solution for this problem through dynamic programming. How many workers require for each period and what is the minimum total cost?

If the cost of each Robust tablet increases to 75 c and the cost of each Vigortab increases to 80 c , find the minimum cost.

If during the following year it is predicted that each comedy skit will generate 30 thousand and each musical number 20 thousand, find the maximum income for the year. A television program director must schedule comedy skits and musical numbers for prime-time variety shows. Each comedy skit requires 2 hours of rehearsal time, costs 3000, and brings in 20,000 from the shows sponsors. Each musical number requires 1 hour of rehearsal time, costs 6000, and generates 12,000. If 250 hours are available for rehearsal and 600,000 is budgeted for comedy and music, how many segments of each type should be produced to maximize income? Find the maximum income.

In Example 3, if the accountant earns a profit of 100 on each individual return and a profit of 175 on each business return, find the maximum profit. An accountant prepares tax returns for individuals and for small businesses. On average, each individual return requires 3 hours of her time and 1 hour of computer time. Each business return requires 4 hours of her time and 2 hours of computer time. Because of other business considerations, her time is limited to 240 hours, and the computer time is limited to 100 hours. If she earns a profit of 80 on each individual return and a profit of 150 on each business return, how many returns of each type should she prepare to maximize her profit?