To allocate a warehouse space of 10,000 square feet to three products A, B, and C, a linear program approach is used. It is given that at least 40% of the space is allocated to product A, at least 20% of the space to product B, and at most 70% of the total space is allocated to A and C collectively. The profits from allocating the space to products A, B and C are $200, $300, and $400 per square foot respectively. Formulate a LP model for this problem to find the optimal allocation Policy.

Ultravision inc. anticipates sales of $280,000 from january through april. materials will represent 50 percent of sales, and because of level production, material purchases will be equal for each month during the four months of january, february, march, and april. materials are paid for one month after the month purchased. materials purchased in december of last year were $24,000 (half of $48,000 in sales). labor costs for each of the four months are slightly different due to a provision in the labor contract in which bonuses are paid in february and april. the labor figures are: january $14,000 february 17,000 march 14,000 april 19,000 fixed overhead is $10,000 per month. prepare a schedule of cash payments for january through april. (assume the $280,000 of sales occur equally over the four months of january through april, i.e. monthly sales = $280,000 / 4.)