Hart manufacturing makes three products. each product requires manufacturing operations in three departments: a, b and c. the labor-hour requirements, by department, are:

department product 1 product 2 product 3
a 1.50 3.00 2.00
b 2.00 1.00 2.50
c 0.25 0.25 0.25

during the next production period, the labor-hours available are 450 in department a, 350 in department b, and 50 in department c. the profit contributions per unit are $25 for product 1, $28 for product 2, and $30 for product 3.
a. formulate a linear programming model for maximizing total profit
b. solve the linear program formulated in part (a) by using excel. include the computer output. how much of each product should be produced and what is the projected total profit contribution?
c. after evaluating the solution obtained in part (a), one of the production supervisors noted that production setup costs had not been taken into account. she noted that setup costs are $400 for product 1, $550 for product 2, and $600 for product 3. if the solution developed in part (b) is to be used, what is the total profit after taking into account the setup costs?
d. management realized that the optimal product mix, taking setup costs into account, might be different from the one recommended in part (b). formulate a mixed integer linear program that takes setup cost into account. management has also stated that we should not consider making more than 175 units of product 1, 150 of product 2, or 140 units of product 3. provide the formulation.
e. solve the mixed integer linear program formulated in part (d) by using excel. include the computer output. how much of each product should be produced and what is the projected profit? compare this profit to that obtained in part (c)

Define the marginal rate of substitution between two goods (x and y). if a consumer’s preferences are given by u(x, y) = x3/4y1/4, compute the consumer’s marginal rate of substitution as a function of x and y. calculate the mrs if the consumer has chosen to consumer 48 units of x and 16 units of y. show your work. (use the back of the page if necessary.

For a firm that uses the weighted average method of process costing, which of the following must be true? (a) physical units can be greater than or less than equivalent units. (b) physical units must be equal to equivalent units. (c) equivalent units must be greater than or equal to physical units. (d) physical units must be greater than or equal to equivalent units.

The starr theater, owned by meg vargo, will begin operations in march. the starr will be unique in that it will show only triple features of sequential theme movies. as of march 1, the ledger of starr showed: cash $3,150, land $22,000, buildings (concession stand, projection room, ticket booth, and screen) $10,000, equipment $10,000, accounts payable $7,300, and owner’s capital $37,850. during the month of march, the following events and transactions occurred. mar. 2 rented the three indiana jones movies to be shown for the first 3 weeks of march. the film rental was $3,600; $1,600 was paid in cash and $2,000 will be paid on march 10.3 ordered the lord of the rings movies to be shown the last 10 days of march. it will cost $200 per night.9 received $4,500 cash from admissions.10 paid balance due on indiana jones movies rental and $2,200 on march 1 accounts payable.11 starr theater contracted with adam ladd to operate the concession stand. ladd is to pay 15% of gross concession receipts, payable monthly, for the rental of the concession stand.12 paid advertising expenses $900.20 received $5,100 cash from customers for admissions.20 received the lord of the rings movies and paid the rental fee of $2,000.31 paid salaries of $2,900.31 received statement from adam ladd showing gross receipts from concessions of $6,000 and the balance due to starr theater of $900 ($6,000 × 15%) for march. ladd paid one-half the balance due and will remit the remainder on april 5.31 received $9,200 cash from customers for admissions.1.) enter the beginning balances in the ledger.2.) journalize the march transactions. starr records admission revenue as service revenue, rental of the concession stand as rent revenue, and film rental expense as rent expense. (credit account titles are automatically indented when the amount is entered. do not indent manually. record journal entries in the order presented in the problem. if no entry is required, select "no entry" for the account titles and enter 0 for the amounts.)3.) post the march journal entries to the ledger. (post entries in the order of journal entries presented in the previous question.)